MtKfltY 

ITRARY 


• 


PLATE  I 


Lirfi.  by  L.PrangsCo.  Boston 


INTRODUCTION 


TO 


PHYSICAL    SCIENCE. 


BY 


A.  P.  GAGE,  PH.D., 

INSTRUCTOR  IN  PHYSICS,  ENGLISH  HIGH  SCHOOL,  BOSTON,  AND 
AUTHOR  or  "  ELEMENTS  OF  PHYSICS." 


BOSTON: 
GINN   &  COMPANY. 

1889. 


WJCATIOI 

Entered  according  to  Act  of  Congress,  in  the  year  1887,  by 

A.  P.  GAGE, 
in  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


TYPOGRAPHY  BY  J.  S.  GUSHING  &  Co.,  BOSTON. 


PRESSWORK    BY    GlNN   &  Co.,   BOSTON. 

Add  to  Lib. 


IDUC 
UBRARY 


AUTHOR'S   PREFACE. 


AN  experience  of  about  six  years  in  requiring  individual 
laboratory  work  from  my  pupils  has  constantly  tended  to 
strengthen  my  conviction  that  in  this  way  alone  can  a  pupil 
become  a  master  of  the  subjects  taught.  During  this  time 
I  have  had  the  satisfaction  of  learning  of  the  successful 
adoption  of  laboratory  practice  in  all  parts  of  the  United 
States  and  the  Canadas ;  likewise  its  adoption  by  some  of 
the  leading  universities  as  a  requirement  for  admission.  Mean- 
time my  views  with  reference  to  the  trend  which  should  be 
given  to  laboratory  work  have  undergone  some  modifications. 
The  tendency  has  been  to  some  extent  from  qualitative  to  quan- 
titative work.  With  a  text-book  prepared  on  the  inductive  plan, 
and  with  class-room  instruction  harmonizing  with  it,  the  pupil  will 
scarcely  fail  to  catch  the  spirit  and  methods  of  the  investiga- 
tor, while  much  of  his  limited  time  may  profitably  be  expended 
in  applying  the  principles  thus  acquired  in  making  physical 
measurements. 

A  brief  statement  of  my  method  of  conducting  laboratory 
exercises  may  be  of  service  to  some,  until  their  own  experience 
has  taught  them  better  ways.  As  a  rule,  the  principles  and 
laws  are  discussed  in  the  class-room  in  preparation  for  subse- 
quent work  in  the  laboratory.  The  pupil  then  enters  the  labo- 
ratory without  a  text-book,  receives  his  note-book  from  the 
teacher,  goes  at  once  to  any  unoccupied  (numbered)  desk 
containing  apparatus,  reads  on  a  mural  blackboard  the  ques- 
tions to  be  answered,  the  directions  for  the  work  to  be  done 
with  the  apparatus,  measurements  to  be  made,  etc.  Having 
performed  the  necessary  manipulations  and  made  his  observa- 

927 


IV 

tions,  he  surrenders  the  apparatus  to  another  who  may  be  ready 
to  use  it,  and  next  occupies  himself  in  writing  up  the  results 
of  his  experiments  in  his  note-book.  These  note-books  are 
deposited  in  a  receptacle  near  the  door  as  he  leaves  the  labo- 
ratory. Nothing  is  ever  written  in  them  except  at  the  times 
of  experimenting.  These  books  are  examined  by  the  teacher  ; 
they  contain  the  only  written  tests  to  which  the  pupil  is  sub- 
jected, except  the  annual  test  given  under  the  direction  of  the 
Board  of  Supervisors.  Pupils,  in  general,  are  permitted  to  com- 
municate with  their  teacher  only.  "Order,  Heaven's  first 
law,"  is  absolutely  indispensable  to  a  proper  concentration  of 
thought  and  to  successful  work  in  the  laboratory. 

Only  in  exceptional  cases,  such  as  work  on  specific  gravity 
and  electrical  measurements,  has  it  been  found  necessary  to 
duplicate  apparatus.  The  same  apparatus  may  be  kept  on  the 
desks  through  several  exercises,  or  until  every  pupil  has  had 
an  opportunity  of  using  it.  Ordinarily  two  pupils  do  not  per- 
form the  same  kind  of  experiment  at  the  same  time.  With 
proper  system,  any  teacher  will  find  his  labors  lighter  than 
under  the  old  elaborate  leiture  system  ;  and  he  will  never  have 
occasion  to  complain  ofQiaclt\fyiitekesi  ^n  the  part  of  his  pupils. 

I  venture  to  hope,  in  viejr  of  the  kind  and' generous  reception 
given  to  the  Elements  01  Physies,Vfcat  this  attempt  to  make 
the  same  methods  availa^bl^  ife  ^somewhat  more  elementary 
work  may  prove  welcome  and^ielpful.  It  has  been  my  aim 
in  the  preparation  of  this  book  to  adapt  it  to  the  requirements 
and  facilities  of  the  average  high  school.  With  this  view,  1 
have  endeavored  to  bring  the  subjects  taught  within  the  easy 
comprehension  of  the  ordinary  pupil  of  this  grade,  without 
attempting  to  "popularize"  them  by  the  use  of  loose  and 
unscientific  language  or  fanciful  and  misleading  illustrations 
and  analogies,  which  might  leave  much  to  be  untaught  in  after 
time.  Especially  has  it  been  my  purpose  to  carefully  guard 
against  the  introduction  of  any  teachings  not  in  harmony  with 
the  most  modern  conceptions  of  Physical  Science. 


I  would  here  acknowledge,  in  a  very  particular  manner,  my 
obligations  for  invaluable'  assistance  rendered  by  Dr.  C.  S. 
Hastings,  Professor  of  Physics  in  the  Sheffield  Scientific  School, 
New  Haven,  Conn.,  and  Prof.  S.  W.  Holman,  of  the  Massa- 
chusetts Institute  of  Technology,  both  of  whom  have  care- 
fully read  all  the  proof-sheets.  It  would,  however,  be  highly 
improper  to  attribute  to  them  in  any  measure  responsibility 
for  whatever  slips  or  inaccuracies  may  have  crept  into  these 
pages.  I  am  also  under  obligations  for  valuable  suggestions  and 
criticisms  received  from  the  veteran  educator,  Prof.  B.  F.  Tweed, 
of  Cambridge,  Mass. ;  George  Weitbrecht,  High  School,  St. 
Paul,  Minn.  ;  John  F.  Woodhull,  Normal  School,  New  Paltz, 
N.Y. ;  Robert  Spice,  Professor  of  Physics  in  the  Technological 
Institute,  Brooklyn,  N.Y.  ;  C.  Fessenden,  High  School,  Napance, 
Ont. ;  A.  H.  McKay,  High  School,  Pictou,  N.S. ;  and  F.  W. 
Gilley,  High  School,  Chelsea,  Mass. 


CONTENTS. 


CHAPTER  I. 

PAGE 

Matter,  energy,  motion,  and  force.  —  Attraction  of  gravitation. — 

Molecular  and  molar  forces  1 


CHAPTER  II. 

Dynamics  of  fluids. — Pressure  in  fluids. — Barometers.  —  Com- 
pressibility and  elasticity  of  gases. — Buoyancy  of  fluids. — 
Density  and  specific  gravity  .  . 29 

CHAPTER  III. 

General  dynamics.  —  Momentum,  and  its  relation  to  force.  —  Three 
laws  of  motion. — Composition  and  resolution  of  forces.— 
Center  of  gravity.  — Falling  bodies.  —  Curvilinear  motion.  — 
The  pendulum 67 

CHAPTER   IV. 

Work  and  energy.  —  Absolute  system  of  measurements.  —  Ma- 
chines   98 

CHAPTER  V. 

Molecular  energy,  heat.  —  Sources  of  heat.  —  Temperature. — 
Effects  of  heat.  —  Thermometry.  —  Convertibility  of  heat.  — 
Thermo-dynamics.  —  Steam-engine 121 


Vlll  CONTENTS. 


CHAPTER  VI. 

PAGE 

Electricity  and  magnetism.  — Potential  and  electro-motive  force. 

—  Batteries.  —  Effects  produced  by  electric  current.  —  Elec- 
trical measurements.  —  Resistance  of   conductors.  —  C.G.S. 
magnetic    and    electro-magnetic    units.  —  Galvanometers.  — 
Measuring    resistances.  —  Divided     circuits ;     methods    of 
combining  voltaic  cells. — Magnets  and  magnetism.  —  Cur- 
rent and  magnetic  electric  induction.  —  Dynamo-electric  ma- 
chines.—  Electric  light. — Electroplating  and  electro  typing. 

—  Telegraphy.  —  Telephony.  —  Thermo-electric    currents.  — 
Static  electricity.  —  Electrical  machines 154 

CHAPTER  VII. 

Sound.  —  Study  of  vibrations  and  waves.  —  Sound-waves,  veloc- 
ity of ;  reflection  of ;  intensity  of ;  ree'nf orcement  of ;  inter- 
ference of.  — Pitch.  —  Vibration  of  strings.  —  Overtones  and 
harmonics.  — Quality.  —  Composition  of  sonorous  vibrations. 

—  Musical  instruments.  —  Phonograph. — Ear 238 

CHAPTER  VIII. 

Radiant  energy,  ether-waves,  light.  —  Photometry.  — Reflection  of 
light-waves.  —  Refraction.  —  Prisms  and  lenses.  —  Prismatic 
analysis.  —  Color.  —  Thermal  effects  of  radiation.  —  Micro- 
scope and  telescope. —  Eye.  —  Stereopticon 281 

APPENDIX:   A,  metric  system;    B,  table  of  specific  gravity;  C, 

table  of  natural  tangents ;  D,  table  of  specific  resistances    .    341 

INDEX  349 


Nature  is  the  Art  of  God."  —  THOMAS  BROWNE. 


CHAPTER   I. 

MATTER,   ENERGY,   MOTION,   AND  FORCE. 

Section  I. 

MATTER   AND   ENERGY. 

To  THE  TEACHER  :  —  That  portion  of  this  book  which  is  printed  in  the 
larger  type,  including  the  experiments,  is  intended  to  constitute  in  itself  a  tolerably 
full  and  complete  working  course  in  Physics.  The  portion  in  fine  print  may, 
therefore,  be  wholly  omitted  without  serious  detriment ;  or  parts  of  it  may 
be  studied  at  discretion  as  time  may  permit;  or,  perhaps  still  better,  it 
may  be  used  by  the  student,  in  connection  with  works  of  other  authors, 
as  subsidiary  reading.  It  should  be  borne  in  mind  that  recitations  from 
memory  of  mere  descriptive  Physics  and  Chemistry  is  of  little  educational 
value. 

To  THE  PUPIL  :  —  "  Read  nature  in  the  language  of  experiment " ; 
that  is,  put  your  questions,  when  possible,  to  nature  rather  than  to  per- 
sons. Teachers  and  books  may  guide  you  as  to  the  best  methods  of 
procedure,  but  your  own  hands,  eyes,  and  intellect  must  acquire  the 
knowledge  directly  from  nature,  if  you  would  really  know. 

1.  Matter.  —  Physics  including  Chemistry,  may  for  the 
present  purposes  at  least  be  regarded  as  the  science  of  mat- 
ter and  energy.     The  question,  What  is  matter  ?  is  appar- 
ently a  very  simple  one,  and  easy  to  answer.     One  of  the 
first  answers  that  will  occur  to  many  is,  Anything  that 
can  be  seen  is  matter. 

2.  Is  Matter  ever  Invisible  ?  —  We  are  usually  able  to 
recognize  matter  by  seeing  it.     We  wish  to  ascertain  by 


MATTER,   ENERGY,   MOTION,   AND  FORCE. 


experiment,  i.e.  by  putting  the  question  to  nature,  whether 
matter  is  ever  invisible.  Now  in  experimenting  there 
must  (1)  be  certain  facts  of  which  we  are  tolerably  cer- 
tain at  the  outset.  These  facts  (2)  lead  us  to  place  things 
in  certain  situations  (the  operation  is  called  manipulation) 
in  order  to  ascertain  what  results  will  follow.  Then,  in 
the  light  of  these  results  we  (3)  reason  from  the  things 
previously  known  to  things  unknown,  i.e.  to  facts  which  we 
wish  to  ascertain. 

For  example,  we  are  certain  that  we  cannot  make  our 
two  hands  occupy  the  same  space  at  the  same  time.     All 


Fig.  1. 


Fig.  3. 


experience  has  taught  us  that  no  two  portions  of  matter  can 
occupy  the  same  spac-e  at  the  same  time.  This  property 
(called  impenetrability)  of  occupying  space,  and  not  only 
occupying  space,  but  excluding  all  other  portions  of  matter 
from  the  space  which  any  particular  portion  may  chance 
to  occupy,  is  peculiar  to  matter;  nothing  but  matter 
possesses  it.  This  known,  we  have  a  key  to  the  solution 
of  the  question  in  hand- 


MATTER   AND   ENERGY. 


3 


There  is  something  which  we  call  air.  It  is  invisible. 
Is  air  matter?  Is  a  vessel  full  of  it  an  "empty"  vessel 
as  regards  matter  ? 


Fig.  3. 


Experiment  1.  —  Thrust  one  end  of  a  glass  tube  to  the  bottom  of 
a  basin  of  water;  blow  air  from  the  lungs  through  the  tube,  and 
watch  the  ascending  bubbles.  Do  you  see  the  air  of  the  bubbles,  or 
do  you  see  certain  spaces  from  which  the  air  has  excluded  the  water? 


MATTER,  ENERGY,  MOTION,  AND  FORCE. 

Is  air  matter  ?    Is  matter  ever  invisible  ?    State  clearly  the  argument 
by  which  you  arrive  at  the  last  two  conclusions. 

Experiment  2.  —  Float  a  cork  on  a  surface  of  water,  cover  it  with 
a  tumbler  (Fig.  1)  or  a  tall  glass  jar  (Fig.  2),  and  thrust  the  glass 
vessel,  mouth  downward,  into  the  water.  (In  case  a  tall  jar  is  used, 
the  experiment  may  be  made  more  attractive  by  placing  on  the  cork 
a  lighted  candle.)  State  what  evidence  the  experiment  furnishes 
that  air  is  matter. 


Relying  upon  the  impenetrability  of  air,  men  descend  in  diving-bells 

(Fig.  3)  to  considerable  depths 
in  the  sea  to  explore  its  bot- 
tom, or  to  recover  lost  prop- 
erty. 

Observe  the  cloud  (Fig.  4) 
formed  in  front  of  the  noz- 
zle of  a  boiling  tea-kettle. 
All  the  matter  which  forms 
the  large  cloud  escapes  from 
the  orifice,  yet  it  is  invisible 
at  that  point,  and  only  be- 
comes visible  after  mingling 
with  the  cold  outside  air. 
Place  the  flame  of  an  alcohol 
lamp  in  the  cloud ;  the  matter 
again  becomes  nearly  or  quite  invisible  in  vicinity  of  the  flame.  True 
steam  is  never  visible.  Here  we  see  matter  undergoing  several  changes  from 
the  visible  to  the  invisible  state,  and  vice  versa. 

3.   Matter,  and  only  Matter,  has  Weight.  —  Has  air 


Experiment  3.  —  Suspend  from  a  scale-beam  a  hollow  globe,  a 
(Fig.  5),  and  place  on  the  other  end  of  the  beam  a  weight,  b  (called  a 
counterpoise),  which  just  balances  the  globe  when  filled  with  air  in 
its  usual  condition.  Then  exhaust  the  air  by  means  of  an  air-pump, 
or  (if  the  scale-beam  is  very  sensitive)  by  suction  with  the  mouth. 
Having  turned  the  stop-cock  to  prevent  the  entrance  of  air,  replace 
the  globe  on  the  beam,  and  determine  whether  the  removal  of  air 
has  occasioned  a  loss  of  weight.  If  air  has  weight,  what  ought  to 


MATTER  AND  ENEKGY. 


be  the  effect  on  the  scale-beam  if  you  open  the  stop-cock  and  admit 
air?  Try  it.  Can  matter  exist  in  an  invisible  state?  How  does 
nature  answer  this  question  in  the  last  experiment? 

4.  Energy.  —  Bodies  of  matter  may  possess  the  ability 
to  put  other  bodies  of  matter  in  motion ;  e.g.  the  bended 
bow  can  project  an  arrow,  and  the  spring  of  a  watch  when 
closely  wound  can  put  in  motion  the  machinery  of  a  watch. 
Ability  to  produce  motion  is  called  energy.  Nothing  but 
matter  possesses  energy.  Does  air  ever  possess  energy  ? 


Fig.  5. 


Fig.  6. 


Experiment  4.  — Put  about  one  quart  of  water  into  vessel  A 
(Fig.  6),  called  a  condensing-chamber.  Connect  the  condensing- 
syringe  B  with  it,  and  force  a  large  quantity  of  air  into  the  portion 
of  the  chamber  not  occupied  by  water;  in  other  words,  fill  this 
portion  with  condensed  air.  Close  the  stop-cock  C,  and  attach  the 
tube  D  as  in  the  figure.  Open  the  stop-cock,  and  a  continuous  stream 
of  water  will  be  projected  to  a  great  hight. 

Experiment  5.  —  Remove  any  water  which  may  remain,  and  again 
condense  air  in  the  chamber.  Connect  the  chamber  by  a  rubber  tube 
with  the  nipple  a  of  the  glass  flask  (Fig.  7).  Place  a  little  water  in 
the  neck  of  the  flask,  so  as  to  cover  the  lower  orifice  of  the  rotating 


MATTER,   ENERGY,   MOTION,   AND   FORCE. 


bulb  B.     Slowly  and  carefully  open  the  stop-cock.     The  escaping  air 
will  cause  the  bulb  B  to  rotate  for  a  long  time. 

You  will  not  attempt  to  say  what 
matter  is.  This,  no  one  knows.  You 
may,  however,  give  a  provisional 
(answering  the  present  needs)  defini- 
tion of  matter,  i.e.  draw  the  limiting 
line  between  what  is  matter  and  what 
is  not  matter. 

5.  Minuteness  of  Particles  of  Mat- 
ter.—  If  with  a  knife-blade  you  scrape 
off  from  a  piece  of  chalk  (not  from  a 
blackboard  crayon,  for  this  is  not  chalk) 
a  little  fine  dust,  and  place  it  under  a 
Fig.  7.  microscope,  "you  will  probably  discover 

that  what  seen  with  the  naked  eye 
appear  to  be  extremely  small,  shapeless  particles,  are 
really  clusters  or  heaps  of  shells  and  corals  more  or  less 
broken.  Figure  8 
represents  such  a 
cluster.  Each  of 
these  shells  is  sus- 
ceptible of  being 
broken  into  thou- 
sands of  pieces. 

Reflecting      that  Fig.  8. 

one  of  these  clus- 
ters is  so  small  as  to  be  nearly  invisible,  you  will  readily 
conceive  that  if  one  of  the  shells  composing  a  cluster 
should  be  broken  into  many  pieces,  and  the  pieces  sepa- 
rated from  one  another,  that  they  would  be  invisible  to 
the  naked  eye.  Yet  the  smallest  of  the  particles  into 


MATTER   AND  ENERGY.  7 

which  one  of  these  shells  can  be  broken  by  pounding  or 
grinding  is  enormously  large  in  comparison  with  bodies 
called  molecules,  which,  of  course,  have  never  been  seen, 
but  in  whose  existence  we  have  the  utmost  confidence. 
(For  definition  and  further  discussion  of  the  molecule,  see 
Chemistry,  page  4.)1 

6.  Theory  of  the  Constitution  of  Matter.  —  For  reasons 
which  will  appear  as  our  knowledge  of  matter  is  extended, 
physicists  have  generally  adopted  the  following  theory  of 
the  constitution  of  matter :  Every  body  of  matter  except  the 
molecule  is  composed  of  exceedingly  small  particles,  called 
molecules.     No   two   molecules   of  matter   in   the   universe 
are  in  permanent  contact  with  each  other.     Every  molecule 
is  in  quivering  motion,  moving  back  and  forth  between  its 
neighbors,  hitting  and  rebounding  from  them.      When  we 
heat  a  body  we  simply  cause  the  molecules  to  move  more 
rapidly  through  their  spaces;   so  they  strike  harder  blows 
on   their   neighbors,  and  usually  push   them  away  a  very 
little  ;  hence,  the  body  expands. 

7.  Porosity.  —  If  the  molecules  of  a  body  are  never 
in  contact  except  at  the  instants  of  collision,  it  follows 
that  there  are  spaces  between  them.     These  spaces  are 
called  pores. 

Water  absorbs  air  and  is  itself  absorbed  by  wood,  paper,  cloth,  etc.  It 
enters  the  vacant  spaces,  or  pores,  between  the  molecules  of  these  substances. 
All  matter  is  porous ;  thus  water  may  be  forced  through  the  pores  of  cast 
iron ;  and  gold,  one  of  the  densest  of  substances,  absorbs  liquid  mercury. 

8.  Volume,  Mass,  and  Density.  —  The  quantity  of  space 
a  body  of  matter  occupies  is  its  volume,  and  is  expressed 
in  cubic  inches^  cubic  centimeters,  etc.     The  quantity  of 
matter  in  a  body  is  its  mass,  and  is  expressed  in  pounds, 

1  References  in  this  book  are  made  to  the  Introduction  to  Chemical  Science,  by  R.  P. 
Williams. 


MATTER,   ENERGY,   MOTION,   AND  FORCE. 

ounces,  kilograms,  grams,  etc.  If  you  cut  blocks  of  wood, 
potato,  cheese,  lead,  etc.,  of  the  same  size  and  weigh  them, 
you  will  find  their  weights  to  be  very  different.  From 
this  you  infer  that  equal  volumes  of  different  substances 
contain  unequal  quantities  of  matter.  Those  which  con- 
tain the  greater  quantity  of  matter  in  the  same  volume 


Fig.  9.  Fig.  10. 


are  said  to  be  denser  than  the  others.  By  the  density  of 
a  body  is  meant  its  mass  in  a  unit  of  volume  ;  hence  it  can 
be  expressed  only  by  giving  both  the  units  of  mass  and  the 
unit  of  volume.  For  example,  the  density  of  cast  iron  is 
4.2  ounces  per  cubic  inch,  or  7.2  grams  per  cubic  centi- 
meter ;  the  density  of  gold  is  11  ounces  per  cubic  inch,  or 
19.4,  grams  per  cubic  centimeter.  Which  of  these  two 
metals  is  the  denser? 


MATTER   AND  ENERGY. 

9.   Three  States  of  Matter. 

Experiment  6.  —  Take  a  thin  rubber  foot-ball  containing  very  lit- 
tle air,  close  the  orifice  of  the  ball  so  that  air  cannot  enter  or  escape, 
place  it  under  the  receiver  of  an  air-pump  (Fig.  9),  and  exhaust  the 
air  from  the  receiver.  The  air  within  the  ball  constantly  expands 
until  the  ball  is  completely  inflated  (Fig.  10). 

We  recognize  three  states  or  conditions  of  matter,  viz., 
solid,  liquid,  and  gaseous,  fairly  represented  by  earth, 
water,  and  air.  Every  day  observation  teaches  us  that 
solids  tend  to  preserve  a  definite  volume  and  shape  ;  liquids 
tend  to  preserve  a  definite  volume  only,  their  shape  conforms 
to  that  of  the  containing  vessel;  gases  tend  to  preserve  neither 
a  definite  volume  nor  shape,  but  to  expand  indefinitely. 

Liquids  and  gases  in  consequence  of  their  manifest  ten- 
dency to  flow  are  called  fluids.  Even  solids  possess  the 
property  of  fluidity  to  a  greater  or  less  extent  when  under 
suitable  stress.  Bodies  also  exist  in  intermediate  condi- 
tions between  the  solid  and  liquid,  and  liquid  and  gase- 
ous, so  that  there  is  no  distinct  limit  between  these  states, 
and  the  distinctions  given  above  are  merely  conventional 
(i.e.  growing  out  of  custom). 

Which  of  the  three  states  any  portion  of  matter  assumes  depends  upon 
its  temperature  and  pressure.  Just  as  at  ordinary  pressures  of  the  atmos- 
phere water  is  a  solid  (i.e.  ice),  a  liquid,  or  a  gas  (i.e.  steam),  according  to 
its  temperature,  so  any  substance  may  be  made  to  assume  any  one  of  these' 
forms  unless  a  change  of  temperature  causes  a  chemical  change,  i.e.  causes 
it  to  break  up  into  other  substances.  For  example,  wood  cannot  be  melted, 
because  it  breaks  up  into  charcoal,  steam,  etc.,  before  the  melting-point  is 
reached.  In  order  that  matter  may  exist  in  a  liquid  (and  sometimes  in  a 
solid)  state,  a  certain  definite  pressure  is  required.  Ice  vaporizes,  but  does 
not  melt  (i.e.  liquefy)  in  a  space  from  which  the  air  (and  consequently 
atmospheric  pressure)  has  been  removed.  Iodine  and  camphor  vaporize, 
but  do  not  melt  unless  the  pressure  is  greater  than  the  ordinary  atmos- 
pheric pressure.  Charcoal  has  been  vaporized,  but  has  never  been  lique- 
fied, undoubtedly  because  sufficient  pressure  has  never  been  used. 

As  regards  the  temperature  at  which  different  substances  assume  the 


10  MATTER,   ENERGY,   MOTION,   AND  FORCE. 

different  states,  there  is  great  diversity.  Oxygen  and  nitrogen  gases,  or 
air,  —  which  is  a  mixture  of  the  two,  —  liquefy  and  solidify  only  at 
extremely  low  temperatures;  and  then,  only  under  tremendous  pressure. 
On  the  other  hand,  certain  substances,  as  quartz  and  lime,  are  liquefied 
only  by  the  most  intense  heat  generated  by  an  electric  current. 


Section  II. 

RELATIVE  MOTION  AND   RELATIVE  REST. 

1C.    What  constitutes  Relative  Motion  and  Relative 

Rest  ?  —  Two  boys  walk  toward  each  other,  or  one  boy 
stands,  and  another  boy  walks  either  toward  or  from  him ; 
in  either  case  there  is  a  relative  motion  between  them, 
because  the  length  of  a  straight  line  (which  may  be  imag- 
ined to  be  stretched)  between  them  constantly  changes. 
One  boy  stands,  and  another  boy  walks  around  him  in  a 
circular  path;  there  is  a  relative  motion  between  them, 
because  the  direction  of  a  straight  line  between  them 
constantly  changes.  There  is  relative  rest  between  two 
boys  while  standing,  because  a  straight  line  between  them 
changes  neither  in  length  nor  direction.  Two  boys  while 
running  are  in  relative  rest  so  long  as  neither  the  distance 
nor  the  direction  from  each  other  changes. 

QUESTIONS. 

1.  What  is  wind?    Give  some  evidence  that  it  possesses  energy. 

2.  Give  a  provisional  definition  of  matter. 

3.  What  is  energy? 

4.  What  is  an  experiment?    What  is  manipulation? 

5.  What  is  an  air-bubble?    What  important  lesson  does  a  mere 
bubble  teach  ? 


FORCE.  11 

6.  What  is  impenetrability?     State  several  properties   that   are 
peculiar  to  matter. 

7.  Can  water  be  rendered  invisible  ?    How  ? 

8.  Under  what  conditions  would  a  flock  of  birds  over  your  head  be 
at  rest  with  reference  to  your  body?    Would  the  birds  which  com- 
pose the  flock  be  at  rest  with  reference  to  one  another  ?    An  apple 
rests  upon  a  table ;  are  its  molecules  at  rest  ? 

9.  Why  do  all  moving  bodies  possess  energy?    Do  all  molecules 
possess  energy  ? 

10.  A  span  of  horses  harnessed  abreast  are  drawing  a  street  car  on 
a  straight,  level  road.     Is  there  any  relative  motion  between  the  two 
horses?    Between  the  horses  and  the  carriage?    Between  the  team 
and  objects  by  the  wayside  ?     Suppose  them  to  be  travelling  in  a  cir- 
cular path  ;  is  there  relative  motion  between  the  horses  ? 

11.  A  boat  moves  away  from  a  wharf  at  the  rate  of  five  miles  an 
hour.     A  person  on  the  boat's  deck  walks  from  the  prow  toward  the 
stern,  at  the  rate  of  four  miles  an  hour ;  what  is  his  rate  of  motion,  i.e. 
his  velocity,  with  reference  to  the  wharf?    What  is  his  velocity  with 
reference  to  the  boat? 

12.  When  is  there  relative  motion  between  two  bodies? 


• 

Section  III. 

FORCE. 

11.  Pushes  and  Pulls.  —  We  are  familiar  with  the 
results  of  muscular  force  in  producing  motion.  We  are 
also  aware  that  there  are  forces,  or  causes  of  motion,  quite 
independent  of  man ;  e.g.,  the  force  exerted  by  wind, 
running  water,  and  steam.  If  we  observe  carefully,  we 
shall  find  that  all  motions  are  produced  by  pushes  or  pulls. 
It  is  evident  that  there  can  be  no  push  or  pull  except  be- 
tween at  least  two  bodies  or  two  parts  of  the  same  body. 


12  MATTER,   ENERGY,   MOTION,   AND  FORCE. 

Commonly,  the  bodies  between  which  there  is  a  push  or 
a  pull  are  either  in  contact,  as  when  we  push  or  pull  a 
table,  or  the  action  is  accomplished  through  an  intermedi- 
ate body,  as  when  we  draw  some  object  toward  us  by 
means  of  a  string,  or  push  an  object  away  with  a  pole. 
Can  two  bodies  push  or  pull  without  contact  and  without 
any  tangible  intermediate  body ;  i.e.  is  there  ever  "action 
at  a  distance  "  f 

Experiment  7.  —  Fill  a  large  bowl  or  pail  with  water  to  the  brim. 
Place  on  the  surface  of  the  water  a  half-dozen  (or  more)  floating  mag- 
nets (pieces  of  magnetized  sewing-needles  thrust  through  thin  slices 
of  cork).  Hold  a  bar  magnet  vertically  over  the  water  with  one  end 
near,  but  not  touching,  the  floats ;  the  floats  either  move  toward  or 
away  from  the  magnet.  Invert  the  magnet,  and  the  motions  of  the 
floats  will  be  reversed. 

Notwithstanding  there  is  no  contact  or  visible  connection  between 
the  floats  and  the  magnet,  the  motions  furnish 
conclusive  evidence  that  there  are  pushes  and 
pulls.  The  motions  are  said  to  be  due  to  mag- 
netic force. 

Experiment  8.  —  Suspend  two  pith  balls  by 
silk  threads.  Rub  a  large  stick  of  sealing-wax 
with  a  dry  flannel,  and  hold  it  near  the  balls. 
The  balls  move  to  the  wax  as  if  pulled  by  it, 
and  remain  in  contact  with  it  for  a  time.  Soon 
they  move  away  from  the  wax  as  if  pushed  away. 
Remove  the  wax;  the  balls  do  not  hang  side 
Fig.  11.  by  side  as  at  first,  but  push  each  other  apart 

(Fig.  11).     These  motions  are  said  to  be  due  to  electric  force. 

12.  How  Force  is  Measured. — Pulling  and  pushing 
forces  may  be  strong  or  wreak,  and  are  capable  of  being 
measured.  The  common  spring  balance  (Fig.  12)  is  a 
very  convenient  instrument  for  measuring  a  pulling  force. 
As  usually  constructed,  the  spring  balance  contains  a  spiral 
coil  of  wire,  which  is  elongated  by  a  pull ;  and  the  pulling 


FORCE.  13 

force  is  measured  by  the  extent  of  the  elongation.  It 
may  be  so  constructed  that  an  elongated 
coil  may  be  compressed  by  a  pushing  force; 
and  when  so  constructed  it  serves  to  measure 
a  pushing  force  by  the  degree  of  compression. 
All  instruments  that  measure  force,  however 
constructed,  are  called  dynamometers  (force- 
measures).  Observe  that  force  is  measured  in 
pounds ;  in  other  words,  the  unit  by  which  force 
is  measured  is  called  a  pound.  Fig. 

13.    Equilibrium  of  Forces. 

Experiment  9.  —  Take  a  block  of  wood ;  insert  two  stout  screw- 
eyes  in  opposite  extremities  of  the  block.  Attach  a  spring  balance  to 
each  eye.  Let  two  persons  pull  on  the  spring  balances  at  the  same 
time,  and  with  equal  force,  as  shown  by  their  indexes,  but  in  opposite 
directions.  The  block  does  not  move.  One  force  just  neutralizes  the 
other,  and  the  result,  so  far  as  the  movement  of  the  block,  i.e.  the  body 
acted  on,  is  concerned,  is  the  same  as  if  no  force  acted  on  it.  When 
one  action,  i.e.  one  push  or  pull,  opposes  in  any  degree  another 
action,  each  is  spoken  of  as  a  resistance  to  the  other.  Let /represent 
the  number  of  pounds  of  any  given  force,  and  let  a  force  acting  in 
any  given  direction  be  called  positive,  and  indicated  by  the  plus  (+) 
sign,  and  a  force  when  acting  in  an  opposite  direction  to  a  force 
which  we  have  denominated  positive,  be  called  negative,  and  indicated 
by  the  minus  (— )  sign.  Then  if  two  forces  +/and  — /  acting  on  a 
body  at  the  same  point  or  along  the  same  line  are  equal,  the  result  is 
that  no  change  of  motion  is  produced. 

Viewed  algebraically,  +/— /=  0 ;  or,  correctly  interpreted,  +/— /== 
(is  equivalent  to)  0,  i.e.  no  force.  In  all  such  cases  there  is  said  to 
be  an  equilibrium  of  forces,  and  the  body  is  said  to  be  in  a  state  of  equi- 
librium. If,  however,  one  of  the  forces  is  greater  than  the  other,  the 
excess  is  spoken  of  as  an  unbalanced  force,  and  its  direction  is  indi- 
cated by  one  or  the  other  sign,  as  the  case  may  be.  Thus,  if  a  force 
of  -f  8  pounds  act  on  a  body  toward  the  east,  and  a  force  of  —  10  pounds 
act  on  the  same  body  along  the  same  line  toward  the  west,  then,  the 
unbalanced  force  is  —2  pounds,  i.e.  the  result  is  the  same  as  if  a 
force  of  only  2  pounds  acted  on  the  body  toward  the  west. 


14       MATTER,  ENERGY,  MOTION,  AND  FORCE. 

14.    Stress,  Action,  and  Reaction ;  Force  Defined.  — 

An  unbalanced  force  always  produces  a  change  of  motion. 
As  there  are  always  two  bodies  or  two  parts  of  a  body  con- 
cerned in  every  push  or  pull,  there  must  be  two  bodies  or 
parts  of  a  body  affected  by  every  push  or  pull.  When  the 
effects  on  both  parties  to  an  action  are  considered  with- 
out special  reference  to  either  alone,  the  force  is  fre- 
quently called  a  stress.  But  when  we  consider  the  effect 
on  only  one  of  two  bodies,  we  find  it  convenient,  and 
almost  a  necessity,  to  speak  of  the  effect  as  due  to  the 
action  of  some  other  body,  or,  still  more  conveniently,  to  an 
external  force.  The  body  which  acts  upon  another,  itself 
experiences  the  effect  of  the  reaction  of  the  same  force. 

We  may  say,  provisionally,  that  force  is  that  ivhich  tends 
to  produce  or  change  motion.  Bringing  a  body  to  relative 
rest  is  changing  its  rate  of  motion  and  requires  force. 
This  definition  of  force  conveys  no  idea  of  what  force  is  ; 
it  merely  distinguishes  between  what  is  force  and  what  is 
not  force. 


QUESTIONS. 

1.  Give  a  provisional  definition  of  force.     In  what  two  ways  is  it 
exerted  ? 

2.  How  is  motion  produced?    Destroyed?    Changed  in  any  way? 

3.  How  many  bodies  or  parts  of  a  body  must  be  concerned  in  the 
action  of  any  single  force  ?     How  many  are  affected  thereby  ? 

4.  What  effect  does  an  unbalanced  force  produce  on  a  body  ? 

5.  How  must  the  magnitude  of  two  forces  compare,  and  in  what 
directions  must  they  act  with  reference  to  each  other,  that  they  may  be 
in  equilibrium  ? 

6.  When  is  a  body  in  equilibrium  ? 

7.  In  what  units  is  force  estimated?    In  what  units  is  mass  esti- 
mated?     What  force  is  required  to  support  10  pounds  of  sugar? 
What  is  the  common  way  of  judging  of  the  mass  of  a  body  ? 


ATTBACTION  OF  GRAVITATION.  15 

8.  Why  will  not  a  force  of  10  pounds  raise  10  pounds  of  sugar  ? 
If  the  force  produces  no  change  of  motion,  how  can  it  consistently  be 
called  a  force  ? 

9.  A  bullet  is  flying  unimpeded  through   space;  does  it  possess 
energy?     Is  it  (disregarding  the  force  of  gravity)  exerting  force? 
Would  it  exert  force  if  it  should  encounter  some  other  body?     Which 
produces  motion,  energy  or  force  ?    Which  denotes  ability  to  produce 
motion  ? 


Section  IV. 

ATTRACTION   OF   GRAVITATION. 

15.  Gravitation  is  Universal.  —  An  unsupported  body 
falls  to  the  earth.     This  is  evidence  of  an  action  or  stress 
between  the  earth  and  the  body.     It  has  been  ascertained 
by  careful  observation  that  when  a  ball  is  suspended  by 
a  long  string  by  the  side  of  a  mountain,  the  string  is 
not  quite  vertical,  but  is  deflected  toward  the  mountain  in 
consequence  of  an  attraction  between  the  mountain  and 
the   ball.     That  there  is  an  attraction  between  the  sun 
and  the  earth,  and  the  earth  and  the  moon,   is  shown,  as 
we  shall   see   further   on,   by   their   curvilinear   motions. 
Tides  and  tidal  currents  on   the   earth   are   due  to  the 
attraction  of  the  sun  and  the  moon. 

This  attraction  is  called  gravitation ;  the  force  is  called 
gravity.  When  bodies  under  its  influence  tend  to  ap- 
proach one  another,  they  are  said  to  gravitate.  Since 
this  attraction  ever  exists  between  all  bodies,  at  all  dis- 
tances, it  is  called  universal  gravitation. 

16.  Law   of    Universal    Gravitation.  —  Methods   too 
difficult  for   us   to   comprehend   at   present   have   estab- 


16  MATTER,    ENERGY,    MOTION,    AND   FORCE. 

lished  the  fact  that  the  strength  of  the  attraction  between 
any  two  bodies  depends  upon  two  things;  viz.,  their 
masses,  and  the  distance  between  certain  points  within 
the  bodies  (to  be  explained  hereafter),  called  their  cen- 
ters of  gravity.  The  following  law  is  found  everywhere 
to  exist :  — 

The  attraction  between  every  two  bodies  of  matter  in  the 
universe  varies  directly  as  the  product  of  their  masses,  and 
inversely  as  the  square  of  the  distance  between  their  centers 
of  gravity.  Representing  the  masses  of  two  bodies  by 
m  and  m',  the  distance  by  d,  and  the  attraction  by  g, 
this  relation  is  expressed  mathematically,  thus :  g  oc 

(varies  as)  — • — .     For  example,  if  the  mass  of  either  body 

is  doubled,  the  product  (mm1)  of  the  masses  is  doubled, 
and  consequently  the  attraction  is  doubled.  If  the  dis- 
tance between  their  centers  of  gravity  is  doubled,  then 

A2      1\ 

f  ~2  =  -  j  the  attraction  becomes  one-fourth  as  great.   ^ 

The  mass  of  the  moon  is  very  much  less  than  that  of  the  earth  j  hence 
the  force  of  gravity  at  the  surface  of  the  former  is  much  less  than  at  the 
surface  of  the  latter.  A  person  who  could  leap  a  fence  three  feet  high  on 
the  earth,  could,  by  the  exertion  of  the  same  muscular  energy,  leap  a  fence 
18  feet  high  on  the  moon.  A  boy  might  throw  a  stone  a  greater  distance 
on  the  moon  than  a  rifle  can  project  a  bullet  on  the  earth.  The  masses  of 
Jupiter  and  Saturn,  being  so  much  greater  than  that  of  the  earth,  the 
corresponding  greater  attraction  which  they  would  exert  would  so  impede 
locomotion  that  a  person  would  be  able  only  to  crawl  along  as  though  his 
feet  were  weighted  with  lead. 

1 7.  Weight.  —  We  say  that  all  matter  has  weight, 
meaning  that  there  is  an  attraction  between  the  earth  and 
all  kinds  of  matter.  We  say  that  the  weight  of  a  certain 
body  is  ten  pounds,  meaning  that  this  is  the  measure  of 
the  force  of  attraction  between  this  body  and  the  earth. 


ATTRACTION   OF   GRAVITATION.  17 

From  the  law  of  gravitation  we  infer  that  at  equal  dis- 
tances from  the  earth's  center  of  gravity  the  weight  of 
bodies  varies  as  their  masses.  Hence,  when  we  weigh  a  body 
we  measure  at  the  same  time  both  the  force  with  which 
the  earth  attracts  it  and  its  mass ;  and  both  quantities 
are  commonly  expressed  in  units  of  the  same  name.  The 
expression  four  pounds  of  tea  conveys  the  twofold  idea 
that  the  quantity  of  tea  is  four  pounds,  and  that  the  force 
with  which  the  earth  attracts  the  tea  is  four  pounds. 

Again,  we  infer  from  the  law  of  gravitation  (1)  that 
a  body  weighs  more  at  a  given  point  on  the  surface  of  the 
earth  than  at  any  point  above  this  point. 

(2)  That  inasmuch  as  some  points  on  the  earth's  sur- 
face are  nearer  its  center  of  gravity  than  others,  the  same 
body  will  not  have  the  same  weight  at  all  points  on  the  earths 
surface.  A  given  body  stretches  a  spring  balance  less  as 
it  is  carried  from  either  pole  toward  the  equator.  The 
loss  of  weight  due  to  the  increase  of  distance  from  the 
center  of  the  earth  is  -g-fg-  of  its  weight  at  the  poles. 

18.  Point  of  Maximum  Weight.  —  There  is  no  defi- 
nite law  which  determines  the  change  in  the  weight  of  a 
body  when  carried  below  the  surface  of  the  earth.  Ob- 
servation has  shown  that  at  first  a  body  increases  in 
weight  slowly,  in  consequence  of  its  approach  to  the 
earth's  center  of  gravity.  But  at  some  undetermined 
depth,  in  consequence  of  an  increase  of  density  of  the 
earth  toward  its  center,  the  increase  of  weight  must 
cease ;  and  at  this .  point,  consequently,  a  body  has  its 
maximum  weight.  From  this  point  onward  to  the  center 
of  gravity  of  the  earth,  a  body  will  lose  in  weight  as  much  as 
it  would  if  it  were  being  transferred  to  smaller  and  smaller 
earths. 


18  MATTER,   ENERGY,   MOTION,   AND   FORCE. 


QUESTIONS. 

1.  If  the  earth's  mass  were  doubled  without  any  change  of  volume, 
how  would  it  affect  your  weight? 

2.  On  what  principle  do  you  determine  that  the  mass  of  one  body 
is  ten  times  the  mass  of  another  body? 

3.  How  many  times  must  you  increase  the  distance  between  the 
centers  of  two  bodies  that  their  attraction  may  become  one-fourth  ? 

4.  If  a  body  on  the  surface  of  the  earth  is  4,000  miles  from  the 
center  of  gravity  of  the  earth,  and  weighs  at  this  place  100  pounds, 
what  would  the  same  body  weigh  if  it  were  taken  4,000  miles  above 
the  earth's  surface? 

5.  The  masses  of  the  planets  Mercury,  Venus,  Earth,  and  Mars  are 
respectively  very  nearly  as  7,  79,  100,  and  12 ;  assuming  that  the  dis- 
tance between  the  centers  of  the  first  two  is  the  same  as  the  distance 
between  the  centers  of  the  last  two,  how  would  the  attraction  between 
the  first  two  compare  with  the  attraction  between  the  last  two  ? 

6.  What  would  be  the  answer  to  the  last  question  if  the  distance 
between  the  centers  of  the  first  two  were  four  times  the  distance 
between  the  centers  of  the  last  two  ? 

7.  Would  the  weight  of  a  soldier's  knapsack  be  sensibly  less  if  it 
were  carried  on  the  top  of  his  rifle  ? 


Section  V. 

MOLECULAR   FORCES. 

19.  Molecular  Distinguished  from  Molar  Forces; 
Repellent  Force. —  Thus  far  we  have  considered  only 
the  effects  of  the  action  of  bodies  of  sensible  (perceived 
by  the  senses)  size  and  at  sensible  distances.  Have  we 
any  evidence  that  the  molecules  which  compose  these 
bodies  act  upon  one  another  in  a  similar  manner? 


MOLECULAR  FORCES.  19 

If  you  attempt  to  break  a  rod  of  wood  or  iron,  or  stretch 
a  piece  of  rubber,  you  realize  that  there  is  a  force  resisting 
you.  You  reason  that  if  the  supposition  be  true,  that  the 
grains  or  molecules  that  compose  these  bodies  do  not- 
touch  one  another,  then  there^must  be  a  powerful  attrac- 
tive force  between  the  molecules,  to  prevent  their  separa- 
tion. After  stretching  the  rubber,  let  go  one  end;  it 
springs  back  to  its  original  form.  What  is  the  cause  ? 
The  volume  of  most  bodies  is  diminished  by  compression ; 
when  the  pressure  is  removed,  they  recover  to  a  greater 
or  less  extent  their  previous  volume.  What  is  the  cause  ? 

Every  body  of  matter,  with  the  possible  exception  of  the 
molecule,  whether  solid,  liquid,  or  gaseous,  may  be  forced 
into  a  smaller  volume  by  pressure;  in  other  words, 
matter  is  compressible.  When  pressure  is  removed,  the 
body  expands  into  nearly  or  quite  its  original  volume. 
This  shows  two  things :  first,  that  the  matter  of  which  a 
body  is  'formed  does  not  really  fill  all  the  space  which  the 
body  appears  to  occupy  ;  and,  second,  that  in  the  body  is  a 
force  which  resists  outward  pressure  tending  to  compress  it, 
and  expands  the  body  to  its  original  volume  when  pressure  is 
removed.  This  is,  of  course,  a  repellent  force,  and  is 
exerted  among  molecules,  tending  to  push  them  farther 
apart. 

For  convenience,  we  call  bodies  of  appreciable  size 
molar  (massive)  in  distinction  from  molecules  (bodies  of 
very  small  mass).  Action  between  molar  bodies,  usually 
at  sensible  distances,  is  called  molar  force  ;  action  between 
molecules,  always  at  insensible  distances,  is  called  molec- 
ular force. 

2O.  Cohesion,  Tenacity.  —  That  attraction  which  holds 
the  molecules  of  the  same  substance  together,  so  as  to  form 


20  MATTER,   ENERGY,   MOTION,   AND   FORCE. 

larger  bodies,  is  called  cohesion.  It  is  the  attraction  that 
resists  a  force  tending  to  break  or  crush  a  body.  The  tenacity 
of  solids  and  liquids,  i.e.  the  resistance  which  they  offer  to 
being  pulled  apart,  is  due  to  this  attraction.  It  is  greatest 
in  solids,  usually  less  in  liquids,  and  entirely  wanting  in 
gases.  It  acts  only  at  insensible  distances,  and  is  strictly 
molecular.  When  cohesion  is  overcome,  it  is  usually  diffi- 
cult to  force  the  molecules  near  enough  to  one  another  for 
this  attraction  to  become  effective  again.  Broken  pieces 
of  glass  and  crockery  cannot  be  so  nicely  readjusted  that 
they  will  hold  together.  Yet  two  polished  surfaces  of 
glass  or  metal,  placed  in  contact,  will  cohere  quite  strongly. 
Or  if  the  glass  is  heated  till  it  is  soft,  or  in  a  semi-fluid 
condition,  then,  by  pressure,  the  molecules  at  the  two 
surfaces  will  flow  around  one  another,  pack  themselves 
closely  together,  and  the  two  bodies  will  become  firmly 
united.  This  process  is  called  welding.  In  this  manner 
iron  is  welded. 

Cohesive  force  varies  greatly  both  in  intensity  and  its  behavior  in  differ- 
ent substances,  and  even  in  the  same  substances  under  different  circum- 
stances. Modifications  of  this  force  give  rise  to  certain  conditions  of  matter 
designated  as  crystalline  or  amorphous,  hard  or  soft,  flexible  or  rigid,  elastic, 
viscous,  malleable,  ductile,  tenacious,  etc. 

21.    Crystallization. 

Experiment  10.  —  Pulverize  about  three 
ounces  of  alum.  Take  about  a  teacupful  of 
boiling  hot  water  in  a  beaker,  and  sift  into  it 
the  powdered  alum,  stirring  with  a  glass  rod 
as  long  as  the  alum  will  dissolve  readily. 
Then  suspend  in  the  liquid  to  a  little  depth 
one  or  more  threads  from  a  splinter  of  wood 
Fi  13  laid  across  the  top  of  a  beaker  (Fig.  13). 

Place  the  whole  where  it  will  not  be  disturbed, 

and  allow  it  to  cool  slowly.     It  is  well  to  allow  it  to  stand  for  a  day  or 

more. 


MOLECULAR   FORCES. 


21 


Beautiful  transparent  bodies  of  regular  shape  are  formed 
on  the  bottom  and  sides  of  the  beaker  and  probably  on 
the  thread.  They  are  called  crystals,  and  the  process  by 
which  they  are  formed  is  called  crystallization. 

Observe  that  the  crystals  formed  on  the  thread  in  mid- 
liquid  are  much  more  regular  in  shape  than  those  formed 
on  the  surface  of  the  glass.  The  latter  are  flattened,  and 
are  said  to  be  tabular. 

In  a  similar  manner,  obtain  crystals  of  bichromate  of  potash,  blue  vitriol, 
copperas,  etc.  Make  up  a  cabinet  of  crystals,  preserving  them  in  small, 
closely  stoppered  glass  bottles. 

Experiment  11.  —  Thoroughly  clean  a  piece  of  window  glass,  by 
breathing  upon  it,  and  then  rubbing  it  with  a  piece  of  newspaper. 


Fig.   14. 

Warm  the  glass  over  an  alcohol  or  Bunsen  flame,  and  pour  upon  the 
glass  a  strong  solution  of  sal  ammoniac,  or  saltpetre.  Allow  the 
liquid  to  drain  off,  and  hold  the  wet  glass  up  to  the  sunlight,  or  view 
it  through  a  magnifying  glass,  and  watch  the  growth  of  the  crystals. 

Experiment  12.  —  Examine  with  a  magnifying  glass  the  surface 
fracture  of  a  freshly  broken  piece  of  sugar  loaf,  and  observe,  if  any, 
small,  smooth,  glistening  planes  thus  exposed. 

These  planes  are  surfaces  of  small,  imperfectly  formed 
crystals  closely  packed  together,  similar  to  the  imperfect 


22  MATTER,   ENERGY,   MOTION,   AND   FORCE. 

crystals  of  alum,  etc.,  formed  on  the  sides  of  the  beaker. 
Such  bodies  are  said  to  have  a  crystalline  fracture,  and  the 
body  itself  is  said  to  be  crystalline  in  distinction  from 
amorphous  matter  like  glass,  glue,  etc.,  which  furnish  no 
evidence  of  crystalline  structure. 

Very  interesting  illustrations  of  crystallization  are  those  delicate  lace- 
like  figures  which  follow  the  touch  of  frost  on  the  window-pane.  Figure 
14  represents  a  few  of  more  than  a  thousand  forms  of  snowflakes  that  have 
been  discovered,  resulting  from  a  variety  of  arrangement  of  the  water 
molecules. 

Snow  crystals  are  formed  during  free  suspension  of  moisture  in  the  air 
and  without  interference  from  contact  with  any  solid ;  hence  their  per- 
fection of  growth.  If  you  gather  snowflakes,  as  they  fall,  on  cold,  yellow 
glass  and  examine  them  under  a  magnifying  glass,  you  will  find  that  all 
crystals  have  a  primary  type  of  six  rays,  and  hexagonal  outline.  Professor 
Tyndall  has  succeeded  in  so  unravelling  lake  ice  as  to  show  what  he  calls 
"  liquid  flowers  "  in  a  block  of  ice,  thus  proving  that  ice  is  crystalline,  or 
composed  of  a  compact  mass  of  crystals.  (Read  Tyndall's  "Forms  of 
Water.") 

Nature  teems  with  crystals.  Nearly  every  kind  of  matter,  in  passing 
from  the  liquid  state  (whether  molten  or  in  solution)  to  the  solid  state, 
tends  to  assume  symmetrical  forms.  Crystallization  is  the  rule  ;  amorphism, 
the  exception.  You  can  scarcely  pick  up  a  stone  and  break  it  without  find- 
ing the  same  crystalline  fracture. 

The  massive  pillars  of  basaltic  rock  found  in  certain  localities,  for  ex- 
ample, in  Fingal's  Cave  (Fig.  15),  might  in  its  broadest  sense  be  regarded 
as  forms  of  crystallization,  inasmuch  as  they  are  the  result  of  natural 
causes.  These  hexagonal  columns,  however,  probably  resulted  from  great 
lateral  pressure,  exerted  while  cooling,  upon  molten  matter  thrown  up 
ages  ago  by  submarine  volcanoes. 

This  tendency  of  the  molecules  of  matter  to  arrange  themselves  in 
definite  ways  during  solidification  is  attended  usually  with  a  change  of 
volume.  The  molecular  force  exerted  at  such  a  time  is  sometimes  enor- 
mous, so  as  to  burst  the  strongest  vessels.  Hence  our  service  pipes  are 
burst  when  water  is  allowed  to  crystallize  (freeze)  in  them. 

22.  Hardness. 

Experiment  13.  —  Get  specimens  of  the  following  substances :  talc, 
chalk,  glass,  quartz,  iron,  silver,  lead,  copper,  rock-salt,  -and  marble. 
Ascertain  which  cf  them  will  scratch  glass,  and  which  are  scratched 


MOLECULAR   FORCES. 


23 


by  glass,  Which  is  the  softest  metal  that  you  have  tried?  The  hard- 
est? Name  some  metal  that  you  can  scratch  with  a  finger-nail.  See 
if  you  can  scratch  a  piece  of  copper  with  a  piece  of  lead,  and  vice  versa. 
Which  is  softer,  iron  or  lead  ?  Which  is  the  denser  metal  ?  Does 
hardness  depend  upon  density?  What  force  must  be  overcome  in 
order  to  scratch  a  substance  ? 


Fig 


To  enable  us  to  express  degrees  of  hardness,  the  following  table  of 
reference  is  generally  adopted :  — 


MOHR  S    SCALE    OF    HARDNESS. 


1.  Talc. 

2.  Gypsum  (or  Rock-Salt). 

3.  Calcite. 

4.  Fluor-Spar. 

5.  Apatite. 


6.  Orthoclase  (Feldspar). 

7.  Quartz. 

8.  Topaz. 

9.  Corundum. 
10.  Diamond. 


By  comparing  a  given  substance  with  the  substances  in  the  table,  its 
degree  of  hardness  can  be  expressed  approximately  by  one  of  the  numbers 
used  in  the  table.  If  the  hardness  of  a  substance  is  indicated  by  the  num- 
ber 4,  what  would  you  understand  by  it  ? 

23.    Hardening  and  Annealing ;   Flexibility. 

Experiment  14.  —  Get  pieces  of  wire,  each  ten  inches  long,  of  the 
following  metals :  steel,  iron,  spring  brass,  hard  copper,  German  silver, 


24  MATTER,   ENERGY,   MOTION,   AND   FORCE. 

platina,  and  phosphor-bronze.  Place  each  in  an  alcohol  or  Bunsen 
flame,  and  heat  the  wire  near  one  end  to  a  bright  red  glow,  and  then 
thrust  the  heated  part  into  cold  water,  and  suddenly  cool  it.  See 
whether  the  part  thus  treated  bends  more  or  less  readily  than  the 
part  which  has  not  suffered  the  sudden  change.  When  a  body  is 
easily  bent,  i.e.  its  cohesive  force  admits  of  a  hinge-like  movement 
among  its  molecules  without  permanent  separation,  it  is  said  to  be 
flexible.  '  See  whether  the  part  treated  has  been  hardened  or  softened 
by  the  treatment.  The  process  of  rendering  flexible  and  softening  is 
called  annealing. 

Next  heat  the  opposite  ends  of  the  wires  as  before,  and  slowly  (10 
to  15  minutes)  withdraw  the  wires  from  the  flame  by  gradually 
raising  them  above  the  flame,  in  order  that  the  fall  of  temperature  may 
be  very  gradual.  Ascertain  as  before  the  effect  of  this  treatment  on 
the  flexibility  and  hardness  of  each.  Classify  the  substances  as  an- 
nealed by  sudden  cooling,  and  annealed  by  slow  cooling. 

24.  Elasticity. 

Experiment  15. —  Obtain  thin  strips  of  as  many  of  the  following 
substances  as  practicable:  rubber,  different  kinds  of  wood,  ivory, 
whalebone,  steel,  spring  brass  and  soft  brass,  copper,  iron,  zinc,  and 
lead. 

Bend  each  one  of  the  above  strips.  Note  which  completely  unbends 
when  the  force  is  removed.  Arrange  the  names  of  these  substances  in 
the  order  of  the  rapidity  and  completeness  with  which  they  unbend. 

The  property  which  matter  possesses  of  recovering  its  former  shape 
and  volume,  after  having  yielded  to  some  force,  is  called  elasticity. 

25.  Viscosity. 

Experiment  16.  —  Support  in  a  horizontal  position,  at  one  of  its 
extremities,  a  stick  of  sealing-wax,  and  suspend  from  its  free  extrem- 
ity an  ounce  weight,  and  let  it  remain  in  this  condition  several  days, 
or  perhaps  weeks.  At  the  end  of  the  time  the  stick  will  be  found  per- 
manently bent.  Had  an  attempt  been  made  to  bend  the  stick  quickly, 
it  would  have  been  found  quite  brittle.  A  body  which,  subjected  to 
a  stress  for  a  considerable  time,  suffers  a  permanent  change  in  form 
is  said  to  be  viscous.  Hardness  is  not  opposed  to  viscosity.  A  lump 
of  pitch  may  be  quite  hard,  and  yet  in  the  course  of  time  it  will  flatten 
itself  out  by  its  own  weight,  and  flow  down  hill  like  a  stream  of  syrup. 


MOLECULAR   FORCES.  25 

Sealing-wax  and  pitch  may  be  regarded  as  fluids  whose  flow  is  ex- 
tremely slow ;  i.e.  their  viscosity  or  resistance  to  flow  is  very  great. 
Liquids  like  molasses  and  honey  are  said  to  be  viscous,  in  distinc- 
tion from  limpid  liquids  like  water  and  alcohol. 

26.  Malleability  and  Ductility. 

Experiment  17.  —  Place  a  piece  of  lead  on  an  anvil,  or  other  flat 
bar  of  surface,  and  hammer  it.  It  spreads  out  under  the  hammer  into 
sheets,  without  being  broken,  though  it  is  evident  that  the  molecules 
have  moved  about  among  one  another,  and  assumed  entirely  different 
relative  positions.  Heat  a  piece  of  soft  glass  tube  in  a  gas-flame,  and, 
although  the  glass  does  not  become  a  liquid,  it  behaves  very  much  like 
a  liquid,  and  can  be  drawn  out  into  very  fine  threads. 

When  a  solid  possesses  sufficient  fluidity  to  admit  of  being  drawn 
out  into  threads,  it  is  said  to  be  ductile.  When  it  will  admit  of  being 
hammered  or  rolled  into  sheets,  it  is  said  to  be  malleable. 

Platinum  and  gold  are  the  most  malleable  and  ductile  metals.  They 
can  be  drawn  into  wire  finer  than  a  spider's  thread,  or  so  as  to  require 
very  keen  vision  to  see  it.  Gold  can  be  hammered  into  leaves  3  o^Wo  °* 
an  inch  thick.  Some  metals,  like  iron,  are  more  malleable  and  ductile  at 
a  red  heat ;  others,  like  copper,  at  an  ordinary  temperature. 

It  is  remarkable  that  the  tenacity  of  most  metals  is  increased  by  being 
drawn  out  into  wires.  It  would  seem  that,  in  the  new  arrangement  which 
the  molecules  assume,  the  cohesive  force  is  stronger  than  in  the  old. 
Hence  cables  made  of  iron  wire  twisted  together,  so  as  to  form  an  iron 
rope,  are  stronger  than  iron  chains  of  equal  weight  and  length,  and  are 
much  used  instead  of  chains  where  great  strength  is  required. 

27.  Adhesion.  —  If  you  touch  with  your  finger  a  piece 
of  gold-leaf,  it  will  stick  to  your  finger ;  it  will  not  drop 
off,  it  cannot  be  shaken  off;  and  an  attempt  to  pull  it  off 
increases  the  difficulty.     Dust  and  dirt  stick  to  clothing. 
Thrust  your  hand  into  water,  and  it  comes  out  wet.     We 
could   not   pick'  up  anything,  or   hold   anything   in   our 
hands,  were  it  not  that  these  things  stick  to  the  hands. 

Every  minute's  experience  teaches  us  that  not  only  is 
there  an  attractive  force  between  molecules  of  the  same 


26  MATTER,   ENERGY,   MOTION,   AND   FORCE. 

kind  of  matter,  but  there  is  also  an  attractive  force  be- 
tween molecules  of  unlike  matter.  That  force  which  causes 
unlike  substances  to  cling  together  is  called  adhesion.  It  is 
probable  that  there  is  some  adhesion  between  all  substances 
when  brought  in  contact.  Glass  is  wet  by  water,  but  is  not 
wet  by  mercury.  If  a  liquid  adheres  to  a  solid  more  firmly 
than  the  molecules  of  the  liquid  cohere,  then  will  the  solid  be 
wet  by  the  liquid.  If  a  solid  is  not  wet  by  a  liquid,  it  is 
not  because  adhesion  is  wanting,  but  because  cohesion  in 
the  liquid  is  stronger. 

28.  Tension. —  When  a  rubber  band  or  cord  is  pulled  or  stretched, 
it  is  said  to  be  in  a  state  of  tension  (i.e.  of  being  stretched).    The  amount 
of  tension  in  a  string  supporting  a  stone  is  the  weight  of  the  stone.     A 
rubber  balloon  inflated  with  compressed  air  is  in  a  state  of  tension ;  the  air 
within  is  in  a  state  of  unusual  compression.     Gases  are  ever  in  a  state  of 
compression,  since  they  ever  tend  to  expand  without  limit. 

29.  Surface  Tension.  —  The  molecular  forces  of  cohesion  and 
adhesion  give  rise  to  a  remarkable  series  of  phenomena,  especially  obvious 
in  liquids,  known  as  phenomena  of  surface  tension.    The  general  law  gov- 
erning all  of  this  class  of  phenomena  is  that  the  surfaces  of  all  bodies  tend  to 
contract  indefinitely.     Since  solids  are  those  bodies  which  tend  to  resist  any 
force  tending  to  alter  their  shape,  and  gases  have  no  surfaces  of  their  own, 
it  is  obvious  why  liquids  show  the  effects  of   such  a  force  most  readily. 
The  tendency  of  a  surface  of  liquid  to  contract  is  illustrated  in  an  imper- 
fect manner  by  a  stretched  sheet  of  rubber;   the  latter,  however,  has  a 
constantly  decreasing  force  of  contraction  as  it  approaches  its  original  di- 
mensions, and  it  may  have  a  contractile  force  in  only  one  direction,  while 
a  surface  sheet  of  liquid  always  tends  to  contract  with  the  same  force  in- 
dependently of  its  size,  and  it  is  exerted  alike  in  all  directions. 

As  a  consequence  of  this,  every  body  of  liquid  tends  to  assume  the  spherical 
form,  since  fie  sphere  has  less  surface  than  any  other  form  having  equal 
volume.  In  large  bodies  the  distorting  forces  due  to  gravity  are  generally 
sufficient  to  disguise  the  effect ;  but  in  small  bodies,  as  in  drops  of  water  or 
mercury,  it  is  apparent.  Again,  if  the  distorting  effect  of  weight  is  elimi- 
nated in  any  way,  as  by  immersing  a  quantity  of  oil  In  a  mixture  of  water  and 
alcohol  of  its  own  density,  or  by  replacing  the  central  portion  of  the  body 


MOLECULAR  FORCES. 


27 


Fig.  15a. 


by  a  fluid  much  lighter  than  its  own  kind,  as  in  the  case  of  a  soap-bubble, 
the  sphere  is  the  resulting  form. 

Experiment  18. — Form  a  soap-bubble  at  the  orifice  of  the  bowl  of  a 
tobacco  pipe,  and  then,  removing  the  mouth  from  the  pipe,  observe  that 
tension  of  the  two  surfaces  (exterior  and  interior)  of  the  bubble  drives  out 
the  air  from  the  interior  and  finally  the  bubble  contracts  to  a  flat  sheet. 

3O.    Capillary  Phenomena.  —  As  a 

result  of  molecular  action  it  is  found  that  the 
surface  of  a  given  liquid  will  always  meet  a  given 
solid  at  a  definite  angle ;  thus  the  surface  sep- 
arating water  and  air  always  meets  clean  glass 
at  a  very  small  angle  (Fig.  15a)  ;  that  separat- 
ing mercury  and  air  meets  glass  at  an  angle  of 
about  135°.  If  clean  silver  is  substituted  for 
glass,  the  first  angle  becomes  large,  not  far  from 
90°,  while  the  second  would  be  reduced  to  zero  ; 
in  other  words,  the  mercury  creeps  along  the  sur- 
face of  silver,  its  own  air-exposed  surface  being  parallel  with  that  of  the 
silver. 

From  this  it  follows,  that  if  a  glass  tube  be  dipped  into  water,  the  sur- 
face tension  will  cause  the  liquid  to  rise  in  the  bore  of  the  tube  above  its  level 
outside;  while,  on  the  contrary,  if  the  tube  be  dipped  into  mercury,  there 
will  result  a  depression.  These  phenomena  are  known  respectively  as  capil- 
lary ascension  and  capillary  depression. 

If  the  bore  of  the  tube  is  reduced  one-half  in  diameter,  the  lifting  force 
is  reduced  one-half,  but  the  cross-section 
will  be  reduced  to  one-fourth;  hence  in 
order  that  the  weight  of  the  liquid  lifted 
may  be  one-half,  it  must  rise  twice  as  high 

J|  J  as  before.     Thus  we  have  the  law  that  the 

^M  ascension   (or  depression)  of  a  liquid  in  a  cap- 

Jj  |        illary    tube    is    inversely    proportional   to    the 

diameter  of  the  bore. 

Experiment  19.  —  Take  a  clean  glass 
tube  of  capillary  (i.e.  small,  hair-like)  bore, 
and  thrust  one  end  to  a  depth  of  about  a 
quarter  of  an  inch  in  water.  Does  the  water 
ascend  or  descend  a  little  way  in  the  tube  ? 
What  is  the  shape  of  the  surface  of  the  water  in  the  bore  of  the  tube  ?  Is 
the  edge  of  the  water  next  the  tube  on  the  outside  turned  up  or  down  ? 


Fig.  16. 


Fig. 


28  MATTER,   ENERGY,   MOTION,   AND  FORCE. 

Repeat  the  experiment  with  tubes  having  bores  of  different  size.  Do  you 
notice  any  difference  in  the  phenomena  in  the  different  tubes  ?  If  so,  in 
which  are  the  phenomena  most  striking  1 

Repeat  all  the  above  experiments,  and  answer  all  the  above  questions, 
using  mercury  instead  of  water. 

Experiment  20.  —  Pour  a  little  water  into  a  U-shaped  tube  (Fig.  16) . 
one  of  whose  arms  has  a  capillary  bore;  how  does  the  water  behave  in  tin- 
capillary  tube  ?  Four  a  little  mercury  into  another  similar  tube  (Fig.  17)  ; 
how  does  the  mercury  behave  1  Describe  the  up- 
per surfaces  of  both  liquids. 

*  Experiment  21.  —  Wipe  the  surface  of  a  small 

/  cambric    needle    with   an  oily  cloth  and  place  it 

carefully  on  the  surface  of  a  cup  of  water.      The 
water  surface  will  meet  the  oily  surface  at  an  an- 
gle of  about  135°,  and  the  surface  tension  of  the 
Fig.  17a.  liquid  will  act  as  a  supporting  force  as  represented 

by  the  arrows  in  Figure  17a,  and  the  needle  will 
float  in  a  trough-shaped  depression  in  the  liquid  surface. 

QUESTIONS. 

1.  Why  are  pens  made  of  steel  ?     What  moves  the  machinery  of  a 
watch  ?     What  is  the  cause  of  the  softness  of  a  hair  mattress  or  feather- 
bed ?     On  what  does  the  entire  virtue  of  a  spring  balance  depend  1 

2.  What  name  would  you  give  to  the  attraction  which  causes  your 
hands  to  be  wet  by  a  liquid  ?     Is  adhesion  a  molar  or  a  molecular  force  ? 

3.  The  tension  of   a  violin  string  is  2  pounds ;  what  is  meant  by  this 
statement  ? 

4.  Why  are  liquid  drops  round  ?     Why  are  bubbles  round  ? 


CHAPTER  II. 

DYNAMICS1  OF  FLUIDS. 

Section  I. 

PRESSURE   IN   FLUIDS. 

31.  Cause  of  Pressure.  —  We  live  above  a  watery 
ocean  and  at  the  bottom  of  an  exceedingly  rare  and  elas- 
tic aerial  ocean,  called  the  atmosphere,  extending  with  a 
diminishing  density  to  an  undetermined  distance  into 
space.  Every  molecule,  in  both  the  gaseous  and  liquid 
oceans,  is  drawn  toward  the  earth's  center  by  gravity. 
This  gives  to  both  fluids  a  downward  pressure  upon 
everything  on  which  they  rest. 

The  gravitating  action  of  liquids  is  everywhere  appar- 
ent, as  in  the  fall  of  drops  of  rain, 
the  descent  of  mountain  streams, 
and  the  weight  of  water  in  a 
bucket.  But  to  perceive  that  air 
exerts  a  downward  pressure  re- 
quires special  manipulation.  If 
we  lower  a  pail  into  a  well,  it 
fills  with  water,  but  we  do  not 
perceive  that  it  becomes  heavier 
thereby ;  the  weight  of  the  water 
in  the  pail  is  not  felt.  But  when 
we  raise  a  pailful  out  of  the  water,  it  suddenly  appears 

1  Dynamics  is  the  science  which  investigates  the  action  of  force. 


30 


DYNAMICS   OF   FLUIDS. 


heavy.  If  we  could  raise  a  pailful  of  air  out  of  the  ocean  of 
air,  might  not  the  weight  of  the  air  become  perceptible  ? 
If  we  dive  to  the  bottom  of  a  pond  of  water,  we  do  not 
feel  the  weight  of  the  pond  resting  upon  us.  We  do  not 
feel  the  weight  of  the  atmospheric  ocean  resting  upon  us ; 
but  we  should  remember  that  our  situation  with  reference 
to  the  air  is  like  that  of  a  diver  with  reference  to  water. 

32.    Gravity  causes  Pressure  in  All  Directions. 

Experiment  22.  —  Fill  two  glass  jars  (Fig.  18)  with  water,  A  hav- 
ing a  glass  bottom,  B  a  bottom  provided 
by  tying  a  piece  of  sheet-rubber  tightly 
over  the  rim.  Invert  both  in  a  larger 
vessel  of  water,  C.  The  water  in  A  does 
not  feel  the  downward  pressure  of  the 
air  directly  above  it,  the  pressure  being 
sustained  by  the  rigid  glass  bottom.  But 
it  indirectly  feels  the  pressure  of  the  air 
on  the  surface  of  the  water  in  the  open 
vessel,  and  it  is  this  pressure  that  sus- 
tains the  water  in  the  jar.  But  the 
rubber  bottom  of  the  jar  B  yields  some- 
what to  the  downward  pressure  of  the 
air,  and  is  forced  inward. 
Experiment  23.  — Fill  a  glass  tube,  D,  with  water,  keeping  one 

end  in  the  vessel  of  water,  and  a  finger 

tightly  closing  the  upper  end.     Why 

does  not  the  water  in  the  tube  fall? 

Remove  your  finger  from  the   closed 

end.     Why  does  the  water  fall  ? 

Experiment  24.  — Fill    (or  partly 

fill)  a  tumbler  with  water,  cover  the 

top  closely  with   a  card  or  writing-paper,  hold  the  paper  in  place 

with  the  palm  of  the  hand,  and  quickly  invert  the  tumbler  (Fig.  19). 

Why  does  not  the  water  fall  out  ? 
Experiment  25.  —  Force  the  piston  A  (Fig.  20)  of  the  seven-in-one 

apparatus  (so  called  from  the  number  of  experiments  that  may  be 

performed  with  one  piece  of  apparatus)  quite  to  the  closed  end  of  the 


Fig.  19. 


Fig.  20. 


PRESSURE  IN   FLUIDS. 


31 


hollow  cylinder,  and  close  the  stop-cock  B.  Try  to  pull  the  piston  out 
again.  Why  do  you  not  succeed?  Hold  the  apparatus  in  various 
positions,  so  that  the  atmosphere  may  press  down, 
laterally,  arid  up  against  the  piston.  Do  you  dis- 
cover any  difference  in  the  pressure  which  it  re- 
ceives from  different  directions  ? 

Experiment  26.  —  Force  a  tin  pail  (Fig.  21), 
having  a  hole  in  its  bottom,  as  far  as  possible  into 
water,  without  allowing  water  to  enter  at  the  top. 
A  stream  of  water  spurts  through  the  hole.  Why  ? 
Why  does  it  require  so  much  effort  to  force  the  pail 
Fig.  31.  down  into  the  water  ? 

33.  Comparison  of  Pressure  at  the  Same  Depth  in 
Different  Directions. 

Experiment  27. —  Take  a  glass  tube  about  30  inches  long  and 
one-fourth  inch  bore,  and  bend  it  into  the  shape  of  A  (Fig.  22).  Also 
prepare  tubes  like  B  and  C.  Let  the 
bend  a  be  about  half  full  of  water. 
Slowly  lower  the  end  n  into  a  tumbler 
filled  with  water.  The  water  presses 
up  against  the  air  in  the  tube,  and 
the  air  transmits  the  pressure  to  the 
liquid  in  the  bend.  How  is  the  pres- 
sure affected  by  depth?  Does  it 
increase  as  the  depth  ? 

Experiment  28.  —  Connect  c  with 
d  by  means  of  a  rubber  tube,  and 
lower  the  extremity  m  into  the  tum- 
bler of  water.  As  the  tube  is  turned 
up,  the  water  must  now  press  down 
the  tube  against  the  air.  Does  the  downward  pressure  increase  as 
the  depth? 

Experiment  29.  —  Connect  e  with  c,  and  lower  o  into  the  water. 
The  water  now  presses  laterally  (sidewise)  against  the  air.  Does  the 
lateral  pressure  increase  as  the  depth  ? 

Experiment  30.  —  Fill  two  tumblers  with  water,  and  lower  n  into  one 
and  o  into  the  other,  keeping  both  extremities  at  the  same  depth 
in  the  liquids.  How  is  the  liquid  in  the  bend  a  affected  ?  How  do 


Fig.  22. 


32 


DYNAMICS   OF   FLUIDS. 


C  « 


Fig.  33. 


the  upward  and  lateral  pressures  at 
the  same  depth  compare  ? 

Experiment  31.  —  Once  more  con- 
nect c  with  dj  and  lower  n  and  m  to 
the  same  depth  into  the  water  in  the 
two  tumblers.  How  do  the  upward 
and  downward  pressures  at  the  same 
depth  compare?  At  the  same  depth  is 
pressure  equal  in  all  directions  ? 

Experiment  32.  —  Connect  the  two 
brass  tubes  at  the  extremities  F  and  G 
(Fig.  23).  Fill  the  cup  of  the  (eight- 
in-one)  apparatus  with  water,  and  re- 
move the  caps  A,  B,  C,  and  D  from 
the  branch  tubes,  so  as  to  permit  water 
to  escape  from  the  orifices  at  their 
ends.  Does  the  water  issuing  from 
these  orifices  show  a  lateral  pressure  ? 
What  difference  do  you  observe  in  the 
flow  of  water  from  the  different 
orifices?  How  do  you  account  for 
it? 

The  results  of  experiments 
thus  far  show  that  at  every 
point  in  a  body  of  fluid  gravity 
causes  pressure  to  be  exerted 
equally  in  all  directions,  and 
that  in  liquids  the  pressure  in- 
creases as  the  depth  increases. 


MEASUREMENT  OF  ATMOSPHERIC  PRESSURE. 


33 


Section  II. 


MEASUREMENT  OF  ATMOSPHERIC  PRESSURE,  BAROMETERS. 


tube 


84. 


34.    How  Atmospheric  Pressure  is  Measured. 

Experiment    33    (preliminary).  —  Take    a    U-shaped    glass 

(Fig.    24),    half  fill    it  with 

water,  close  one   end  with   a 

thumb,  and  tilt  the  tube  so 

that  the  water  will  run  into 

the   closed    arm    and    fill  it; 

then  restore  it  to  its  original 

vertical  position.      Why  does 

not   the   water  settle    to  the 

same  level  in  both  arms  ? 

Figure  25  represents  a  U-shaped  glass  tube  closed  at  one  end,  34 
inches  in  hight,  and  with  a  bore  of  1  square  inch 
section.  The  closed  arm  having  been  filled  with 
mercury,  the  tube  is  placed  with  its  open  end  up- 
ward, as  in  the  cut.  The  mercury  in  the  closed  arm 
sinks  about  2  inches  to  A,  and  rises  2  inches  in  the 
open  arm  to  C ;  but  the  surface  A  is  30  inches 
higher  than  the  surface  C.  This  can  be  accounted 
for  only  by  the  atmospheric  pressure.  The  column 
of  mercury  BA,  containing  30  cubic  inches,  is  an 
exact  counterpoise  for  a  column  of  air  of  the  same 
diameter  extending  from  C  to  the  upper  limit  of 
the  atmospheric  ocean,  —  an  unknown  hight. 

The  weight  of  the  30  cubic  inches  of  mercury 
in  the  column  BA  is  about  15  pounds.  Hence 
the  weight  of  a  column  of  air  of  1  square-inch  sec- 
tion, extending  from  the  surface  of  the  sea  to  the 
upper  limit  of  the  atmosphere,  is  about  15  pounds. 
But  in  fluids  gravity  causes  equal  pressure  in  all 
directions.  Hence,  at  the  level  of  the  sea,  all  bodies 

are  pressed  upon  in  all  directions  by  the  atmosphere,  with  a  force  of  about 

15  pounds  per  square  inch,  or  about  one  ton  per  square  foot. 


Fig.  25. 


34 


DYNAMICS   OF  FLUIDS. 


A  pressure  of  15  pounds  per  square  inch  is  quite  generally  adopted 
as  a  unit  of  gaseous  pressure,  and  is  called  an  atmosphere. 


JFig.  36. 

35.  Barometer.  —  The  hight  of  the 
column  of  mercury  supported  by  atmos- 
pheric pressure  is  quite  independent,  how- 
ever, of  the  area  of  the  surface  of  the  mer- 
cury pressed  upon ;  hence  the  apparatus 
is  more  conveniently  constructed  in  the 
form  represented  in  Figure  26. 

A  straight  tube  about  34  inches  long 
is  closed  at  one  end  and  filled  with  mer- 
cury. A  finger  tightly  closing  the  open 
end,  the  tube  is  inverted,  and  this  end  is 
inserted  in  a  vessel  of  mercury  and  the 
finger  is  withdrawn,  when  the  mercury  pj 
sinks  until  there  is  equilibrium  between 
the  downward  pressure  of  the  mercurial  column  AB  and 


BAROMETERS.  35 

the  pressure  of  the  atmosphere.  An  apparatus  designed 
to  measure  atmospheric  pressure  is  called  a  barometer 
(pressure-measurer).  A  common  form  of  barometer  is 
represented  in  Figure  27.  Beside  the  tube  and  near  its 
top  is  a  scale  graduated  in  inches  or  centimeters,  indi- 
cating the  hight  of  the  mercurial  column.  For  ordinary 
purposes  this  scale  needs  to  have  only  a  range  of  three  or 
four  inches,  so  as  to  include  the  maximum  fluctuations 
of  the  column. 

The  hight  of  the  barometric  column  is  subject  to  fluc- 
tuations ;  this  shows  that  the  atmospheric  pressure  is  sub- 
ject to  variations.  The  barometer  is  always  a  faithful 
monitor  of  all  changes  in  atmospheric  pressure.  It  is  also 
serviceable  as  a  weather  indicator.  It  does  not  indicate 
weather  that  is  present,  but  foretells  coming  weather. 
Not  that  any  particular  point  at  which  mercury  may  stand 
foretells  any  particular  kind  of  weather,  but  any  sudden 
change  in  the  barometer  indicates  a  change  in  the  weather. 
A  rapid  fall  of  mercury  generally  forebodes  a  storm, 
while  a  rising  column  indicates  clearing  weather. 

36.  Aneroid  Barometer.  —  The  aneroid  (without  moisture) 
barometer  employs  no  liquid.  It  contains  a  cylindrical  box,  D  (Fig. 
28),  having  a  very  flexible  top.  The  air  is  partially  exhausted  from 
within  the  box.  The  varying  atmospheric  pressure  causes  this  top  to 
rise  and  sink  much  like  the  chest  of  man  in  breathing.  Slight  move- 
ments of  this  kind  are  communicated  by  means  of  multiplying-apparatus 
(apparatus  by  means  of  which  a  small  movement  of  one  part  is  mag- 
nified into  a  large  movement  of  another  part)  to  the  index  needle  A. 
The  dial  is  graduated  to  correspond  with  a  mercurial  barometer.  The 
observer  turns  the  button  C  and  brings  the  brass  needle  B  over  the  black 
needle  A,  and  at  his  next  observation  any  departure  of  the  latter  from 
the  former  will  show  precisely  the  change  which  has  occurred  between 
the  observations. 

The  aneroid  can  be  made  more  sensitive  (i.e.  so  as  to  show  smaller 
changes  of  atmospheric  pressure)  than  the  mercurial  barometer.  If  a 


DYNAMICS   OP  FLUIDS. 

barometer  is  carried  up  a  mountain,  it  is  found  that  the  mercury  constantly 
falls  as  the  ascent  increases.  Roughly  speaking,  the  barometer  falls  one 
inch  for  every  900  feet  of  ascent.  Really,  in  consequence  of  the  rapid 
increase  of  the  rarity  of  the  air,  the  rate  of  fall  diminishes  as  you  ascend. 
It  is  obvious  that  the  barometer  will  serve  to  measure  approximately  the 
bights  of  mountains. 


Fig.   88. 

If  a  mercurial  barometer  stand  at  760  mm  on  the  floor,  the  same  barom- 
eter on  the  top  of  a  table  lm  high  should  stand  at  a  hight  of  759.91mm, 
a  change  scarcely  perceptible.  The  aneroid  is,  however,  sometimes  made 
so  sensitive  that  the  change  of  pressure  experienced  in  this  short  distance 
is  rendered  quite  perceptible. 

The  shading  in  Figure  29  is  intended  to  indicate  roughly  the  varia- 
tion in  the  density  of  the  air  at  different  elevations  above  sea-level.  The 
figures  in  the  left  margin  show  the  hight  in  miles ;  those  in  the  first 
column  on  the  right,  the  corresponding  average  hight  of  the  mercurial 


BAROMETERS. 


37 


column  in  inches ;  and  those  in  the  extreme  right,  the  density  of  the  air 
compared  with  its  density  at  sea-level.  The  average  hight  of  the  mer- 
curial column  at  sea- 
level  is  about  30 
inches  (76cm). 

If  an  opening  could 
be  made  in  the  earth, 
35  miles  in  depth  be- 
low the  sea-level,  it 
is  calculated  that  the 
density  of  the  air 
at  the  bottom  would 
be  1,000  times  that 
at  sea-level,  so  that 
water  would  float  in 
it.  Air  has  been  com- 
pressed to  this  den- 
sity. 

To  what  hight  the 
atmosphere  extends 
is  unknown.  It  is 
variously  estimated 
at  from  50  to  200 
miles.  If  the  aerial 
ocean  were  of  uni- 
form density,  and  of 
the  same  density  that 
it  is  at  the  sea-level, 
its  depth  would  be  a 
little  short  of  five 
miles.  Certain  peaks 
of  the  Himalayas 
would  rise  above  it. 

MMiMM^^^^MMV^HH^^H^MH^ 

Fig.  39. 


88  DYNAMICS  OF   FLUIDS. 


Section  III. 

COMPRESSIBILITY  AND  ELASTICITY    OF    GASES.  —  BOYLE'S 

LAW. 

37.  Compressibility  of  Gases.  —  The  increase  of  pres- 
sure attending  the  increase  in  depth,  in  both  liquids  arid 
gases,  is  readily  explained  by  the  fact  that  the  lower  layers 
of  fluids  sustain  the  weight  of  all  the  layers  above.     Con- 
sequently, if  the  body  of  fluid  is  of  uniform  density,  as  is 
very  nearly  the  case  in  liquids,  the  pressure  will  increase 
in  nearly  the  same  ratio  as  the  depth  increases.     But  the 
aerial  ocean  is  far  from  being  of  uniform  density,  in  con- 
sequence of  the  extreme  compressibility  of  gaseous  matter. 
The  contrast  between  water  and  air,  in  this  respect,  may 
be  seen  in  the  fact  that  water  subjected  to  a  pressure  of 
one  atmosphere  contracts  0.0000457  of  its  volume ;  under 
the  same  circumstances,  air  contracts  one-half.     For  most 
practical  purposes,  we  may  regard  the  density  of  water  at 
all  depths  as  uniform,  while  it  is  far  otherwise  in  large 
masses  of  gases. 

38.  Elasticity    of    Gases.  —  Closely   allied    to    com- 
pressibility is   the    elasticity  of  gases,  or  their  power  to 
recover  their  former  volume  after  compression.     The  elas- 
ticity of  all  fluids  is  perfect.     By  this  is  meant,  that  the 
force  exerted  in  expansion  is  equal  to  the  force  used  in 
compression;   and   that,  however  much   a   fluid   is   com- 
pressed, it  will  always  completely  regain  its  former  bulk 
when   the   pressure   is  removed.     Hence   the   barometer 
which  measures  the  compressing  force  of  the  atmosphere 
also  measures  at  the  same  time  the  elastic  force  (i.e.  the 


COMPRESSIBILITY  AND  ELASTICITY  OF  GASES. 


39 


tension  or  expansive  force)  of  the  air.  Liquids  are  per- 
fectly elastic ;  but,  inasmuch  as  they  are  perceptibly  com- 
pressed only  under  tremendous  pressure,  they  are  regarded 
as  practically  incompressible,  and  so  it  is  rarely  necessary 
to  consider  their  elasticity.  It  has  already  been  stated 
that  matter  in  a  gaseous  state  expands  indefinitely  unless 
restrained  by  external  force.  The  atmosphere  is  con- 
fined to  the  earth  by  the  force  of  gravity. 


Experiment  34.  —  Force  the  piston  of  the  seven-in-one  apparatus 

two-thirds  the  way  into  the  cylinder,  and  close  the  aperture.     Support 

the  apparatus  on  blocks,  with  the  piston  upwards,  remove  the  handle, 

and  place  a  weight  on  the  piston,  and  place  the 

whole  under  the  receiver  of  an  air-pump.    Exhaust 

the  air  from  the  receiver ;  the  outside  pressure  of 

the  air  being  partially  removed,  the  unbalanced 

force  (i.e.  the  tension)  of  the  air  enclosed  within 

the  cylinder  will  cause  the  piston  to  rise,  and  raise 

the  weight. 

Experiment  35.  —  Arrange  the  same  apparatus 

as  in  Figure  30.    Attach  a  small  rubber  tube  to 

the  short  tube,  and  suck  as  much  air  out  of  the 

cylinder  as  possible.  The  air  within,  being  rare- 
fied, loses  its  tension,  and  the  unbalanced  outside 
pressure  forces  the  piston  into 
the  cylinder,  raising  the  weight. 
A  very  much  heavier  weight  may  be  raised  if  the 
rubber  tube  connects  the  apparatus  with  an  air- 
pump. 

Experiment  36.  —  Take  a  glass  tube  (Fig.  31) 
having  a  bulb  blown  at  one  end.  Nearly  fill  it 
with  water,  so  that  when  inverted  there  will  be  only 
a  bubble  of  air  in  the  bulb.  Insert  the  open  end 
in  a  glass  of  water,  place  under  a  receiver,  and 
exhaust.  Nearly  all  the  water  will  leave  the  bulb 

and  tube.     Why?     What  will  happen  when  air  is  admitted  to  the 

receiver  ? 


Fig.  30. 


Fig.  31. 


40 


DYNAMICS   OF  FLUIDS. 


39.    Boyle's  or  Mariotte's  Law. 

Experiment  37.  —  Take  a  bent  glass  tube  (Fig.  32),  the  short  arm 
being  closed,  and  the  long  arm,  which  should  be 
at  least  34  inches  (85cm)  long,  being  open  at  the 
top.  Pour  mercury  into  the  tube  till  the  surfaces 
in  the  two  arms  stand  at  zero.  Now  the  surface 
in  the  long  arm  supports  the  weight  of  an  atmos- 
phere. Therefore  the  tension  of  the  air  enclosed 
in  the  short  arm,  which  exactly  balances  it,  must 
be  about  15  pounds  to  the  square  inch.  Next  pour 
mercury  into  the  long  arm  till  the  surface  in  the 
short  arm  reaches  5,  or  till  the  volume  of  air  en- 
closed is  reduced  one-half,  when  it  will  be  found 
that  the  hight  of  the  column  AC  is  just  equal  to 
the  hight  of  the  barometric  column  at  the  time 
the  experiment  is  performed.  It  now  appears 
that  the  tension  of  the  air  in  AB  balances  the 
atmospheric  pressure,  plus  a  column  of  mercury 
AC,  which  is  equal  to  another  atmosphere;  .•.  the 
tension  of  the  air  in  AB  =  two  atmospheres.  But 
the  air  has  been  compressed  into  half  the  space  it 
formerly  occupied,  and  is,  consequently,  twice  as 
dense.  If  the  length  and  strength  of  the  tube 
would  admit  of  a  column  of  mercury  above  the 
surface  in  the  short  arm  equal  to  twice  AC,  the 
air  would  be  compressed  into  one-third  its  original 
bulk ;  and,  inasmuch  as  it  would  balance  a  pres- 
sure of  three  atmospheres,  its  tension  would  be 
Fig.  33.  increased  threefold. 

From  this  experiment  we  learn  that,  at  twice  the  pres- 
sure there  is  half  the  volume,  while  the  density  and  elas- 
tic force  are  doubled.  Hence  the  law :  — 

The  volume  of  a  body  of  gas  at  a  constant  temperature 
varies  inversely  as  the  pressure,  density,  and  elastic  force. 

For  many  years  after  the  announcement  of  this  law  it 
was  believed  to  be  rigorously  correct  for  all  gases,  but 
more  recently,  more  precise  experiments  have  shown  that 


RAREFYING  AND  CONDENSING  INSTRUMENTS.          41 

it  is  approximately  but  not  rigidly  true  for  any  gas,  that 
the  departure  from  the  law  differs  with  different  gases, 
and  that  each  gas  possesses  a  special  law  of  compressibility. 


Section  IV. 

INSTRUMENTS  USED  FOR  RAREFYING  AND  CONDENSING 

AIR.  h 

4O.  The  Air-Pump.  —  The  air-pump,  as  its  name  im- 
plies, is  used  to  withdraw  air  from  a  closed  vessel.  Figure 
33  will  serve  to 
illustrate  its  op- 
eration. R  is  a 
glass  receiver  from 
which  air  is  to  be 
exhausted.  B  is  a 
hollow  cylinder  of 
brass,  called  the 
pump -barrel.  The 
plug  P,  called  a 
piston,  is  fitted  to 
the  interior  of  the 
barrel,  and  can  be  Fis-  33> 

moved  up  and  down  by  the  handle  H ;  s  and  t  are  valves. 
A  valve  acts  on  the  principle  of  a  door  intended  to 
open  or  close  a  passage.  If  you  walk  against  a  door 
on  one  side,  it  opens  and  allows  you  to  pass;  but 
if  you  walk  against  it  on  the  other  side,  it  closes  the 
passage,  and  stops  your  progress.  Suppose  the  piston 
to  ba  in  the  act  of  descending;  the  compression  of 


42 


DYNAMICS  OF   FLUIDS. 


the  air  in  B  closes  the  valve  t,  and  opens  the  valve  », 
and  the  enclosed  air  escapes.  After  the  piston  reaches 
the  bottom  of  the  barrel,  it  begins  its 
ascent.  This  would  cause  a  vacuum  be- 
tween the  bottom  of  the  barrel  and  the 
ascending  piston  (since  the  unbalanced 
pressure  of  the  outside  air  immediately 
closes  the  valve  s),  but  the  tension  of 
the  air  in  the  receiver  R  opens  the 
valve  t  and  fills  this  space.  As  the  air 
in  R  expands  it  becomes  rarefied  and 
loses  some  of  its  tension.  The  external 
pressure  of  the  air  on  R,  being  no  longer 
balanced  by  the  tension  of  the  air  within, 
presses  the  receiver  firmly  upon  the  plate 
L.  Each  repetition  of  a  double  stroke 
of  the  piston  removes  a  portion  of  the 
air  remaining  in  R.  The  air  is  removed 
from  R  by  its  own  expansion.  However 
far  the  process  of  exhaustion  may  be 
carried,  the  receiver  will  always  be  filled 
with  air,  although  it  may  be  exceedingly 
rarefied.  The  operation  of  exhaustion 
is  practically  ended  when  the  tension  of 
the  air  in  R  becomes  too  feeble  to  lift 
the  valve  t. 

Sometimes    another    receiver,   D,    is 
used,  opening  into  the  tube  T,  that  con- 
nects the  receiver  with  the  barrel.    In- 
side the  receiver  is  placed  a  barometer. 
Fig.  34.  It  is  apparent  that  air  is  exhausted  from 

D  as  well  as  from  R;  and,  as  the  pressure  is  removed 
from   the   surface   of  the  mercury  in   the  cup,  the  bar- 


m\ 


RAREFYING  AND  CONDENSING  INSTRUMENTS. 


43 


ometric  column  falls;  so  that  the  barometer  serves  as  a 
gauge  to  indicate  the  approximation  to  a  vacuum.  For 
instance,  when  the  mercury  has  fallen  380 mm  (15  inches), 
one-half  of  the  air  has  been  removed. 


41.   Sprengel  Pump. 

Experiment  38.  —  Remove  the  cap  from  /  (Fig.  34),  and  con- 
nect with  a  glass  tube  &,  about  12  inches  long.  Let  k  dip  into  a  tum- 
bler of  water,  m.  Support  the  ap- 
paratus on  a  couple  of  blocks  of 
wood,  so  that  when  the  stopper  a 
in  the  base  is  removed,  the  water 
may  fall  freely  out  at  the  bottom. 
Fill  the  cup  g  with  water,  and 
allow  it  to  escape  at  a.  As  the 
water  passes  the  branch  tube  /, 
the  expansive  air  in  the  tube  gets 
entangled  in  the  water,  and  is  con- 
stantly removed  by  the  falling 
stream,  and  thus  a  partial  vacuum 
is  formed  in  the  tube  k.  The  pres- 
sure of  air  on  the  surface  of  the 
water  in  the  open  cup  forces  the 
water  up  the  tube  k,  and  empties 
the  tumbler.  If  m  were  a  closed 
vessel  filled  with  air,  it  is  apparent 
that  a  partial  vacuum  would  be 
created  in  it.  An  apparatus  con- 
structed like  this,  in  which  mercury 
is  employed  instead  of  water,  constitutes  one  of  the  most  efficient 
air-pumps  in  use.  It  is  called  the  Sprengel  pump. 

Modifications  of  this  pump  have  extensive  use  in  the  arts,  such  as 
in  obtaining  high  vacua  in  electrical  lamps,  radiometers,  etc.  By  means 
of  a  good  Sprengel  pump  exhaustion  to  the  hundred-millionth  of  an 
atmosphere  can  be  attained.  In  such  a  space  it  is  calculated  that  a 
molecule  of  air  traverses  an  average  distance  of  33  feet  before  colliding 
with  another  molecule  of  air. 


Fig.  35. 


44 


DYNAMICS   OF  FLUIDS. 


42.   Condenser. 

Experiment  39.— Into  the  neck  of  a  bottle  partly  filled  with  watei 
(Fig.  35)  insert  a  cork  very  tightly,  through  which  pass  a  glass  tube 
nearly  to  the  bottom  of  the  bottle.  Blow  forcibly 
into  the  bottle.  On  removing  the  mouth  water 
will  flow  through  the 
tube  in  a  stream. 
Explain. 

Figure  6,  page 
5,  represents  in 
perspective,  and 
Figure  36,  in  sec- 
tion, an  appara- 
tus for  condensing 
air,  called  a  con- 
denser. Its  con- 
Fig,  so.  struction  is  like  Fig'  37' 
that  of  the  barrel  of  an  air-pump,  except  that  the  direc- 
tion in  which  the  valves  open  is  reversed. 

Experiment  40.  —  Place  a  block  having  a  wide  platform  at  one 
end  on  the  piston  of  the  seven-in-one  apparatus.  On  the  platform  let 
a  child  stand.  By  means  of  a  condensing  syringe  (Fig.  6),  connected 
by  a  rubber  tube  with  the  seven-in-one  apparatus  (Fig.  37),  condense 
the  air  in  the  cylinder  and  raise  the  child. 


Section  V. 

APPARATUS  FOR  RAISING  LIQUIDS. 

43.  Lifting  or  Suction  Pump.  —  The  common  lifting- 
pump  is  constructed  like  the  barrel  of  an  air-pump.  Fig- 
ure 38  represents  the  piston  B  in  the  act  of  rising.  As 


APPARATUS  FOR   RAISING  LIQUIDS. 


45 


the  air  is  rarefied  below  it,  water  rises  in  consequence 
of  atmospheric  pressure  on  the  water  in  the  well,  and 
opens  the  lower  valve  D.  Atmospheric  pressure  closes 


Fig.  4O. 

the  upper  valve  C  in  the  piston.  When 
the  piston  is  pressed  down  (Fig.  39),  the 
lower  valve  closes,  the  upper  valve  opens, 
and  the  water  between  the  bottom  of  the 
barrel  and  the  piston  passes  through  the 
Fig.  ss.  upper  valve  above  the  piston.  When 

the  piston  is  raised  again  (Fig.  40),  the  water  above  the 

piston  is  raised  and  discharged  from  the  spout. 
The  liquid  is  sometimes  said  to  be  raised 

in  a  lifting-pump  by  the  "force  of  suction." 

Is  there  such  &  force? 


Experiment  41.  —  Bend  a  glass  tube  into  a  U-shape, 
with  unequal  arms,  as  in  Figure  41.  Fill  the  tube  with 
the  liquid  to  the  level  cb.  Close  the  end  b  with  a  finger, 
and  try  to  suck  the  liquid  out  of  the  tube.  You  find 
it  impossible.  Remove  the  finger  from  b,  and  you  can  suck  the  liquid 
out  with  ease.  Why  ? 


41> 


46 


DYNAMICS   OF  FLUIDS. 


44.  Force-Pump.  —  The  piston  of  a  force-pump  (Fig. 
42)  has  no  valve,  but  a  branch  pipe  a  leads  from  the  lower 
part  of  the  barrel  to  an  air-condensing  chamber  6,  at  the 
bottom  of  which  is  a  valve  £,  opening  upward.  As  the 
piston  is  raised,  water  is  forced  up  through 
the  valve  d,  while  water  in  b  is  pre- 
vented from  returning  by  the  valve  c. 
When  the  piston  is  forced  down,  the 
valve  d  closes,  the  valve  c  opens,  and  the 
water  is  forced  into  the  chamber  5,  con- 
densing the  air  above  the  water.  The 
elasticity  of  the  condensed  air  forces  the 
ID  water  out  of  the  tube  e  in  a  continuous 
stream. 

QUESTIONS  AND  PROBLEMS. 

1.  What  force  is  the  cause  of  fluid  pressure? 

2.  Why  does  not  a  person  at  the  bottom  of  a 
pond  feel  the  weight  of  the  water  above  him  ? 

3.  An  aeronaut  finds  that  on    the  earth  his 
barometer  stands  at  30  inches.     He  ascends  in  a 
balloon  until  the  barometer  stands  at  20  inches. 
About  how  high  is  he  ?     What  is  the  pressure  of 
the  atmosphere  at  his  elevation  ? 

4.  When  a  barometer  stands  at  30  inches,  the 
atmospheric  pressure  is  14.7  pounds.      What  is 

the  atmospheric  pressure  when  the  barometer  stands  at  29  inches? 

5.  Why  is  a  barometer  tube  closed  at  the  top  ?    Why  must  air  come 
in  contact  with  the  mercury  at  the  bottom? 

6.  What  would  be  the  effect  on  an  aneroid  barometer  if  it  were 
placed  under  the  receiver  of  an  air-pump,  and  one   or  two  strokes 
of  the  pump  were  made? 

7.  Suppose  a  rubber  foot-ball  to  be  partially  inflated  with  air  at 
the  surface  of  the  earth ;  what  would  happen  if  it  were  taken  up  in  a 
balloon  ? 

8.  Mercury  is  13.6  times  denser  than  water.    When  a  mercurial  ba- 


Fig.  43, 


TRANSMISSION   OF  EXTERNAL  PRESSURE.  47 

rometer  stands  at  30  inches,  how  high  would  a  water  barometer  stand  ? 
How  high,  theoretically,  could  mercury  be  raised  on  such  a  day  by 
suction?  How  high  could  water  be  raised  by  the  same  means ?  How 
many  times  higher  can  water  be  raised  by  a  suction-pump  than  mer- 
cury? 

9.  What  is  that  which  is  sometimes  called  the  "  force  of  suction  "  ? 

10.  The  area  of  one  side  of  the  piston  of  the  seven-in-one  apparatus 
is  about  26  square  inches.    Suppose  the  piston  to  be  forced  into  the 
cylinder  so  as  to  drive  out  all  the  air,  and  then  the  orifice  to  be  closed ; 
what  force  would  be  required  to  draw  the  piston  out,  when  the  barom- 
eter stands  at  30  inches  ?    What  force  would  be  required  on  the  top  of 
a  mountain  where  the  barometer  stands  at  15  inches  ? 

11.  Water  is  raised  the  larger  part  of  the  distance  in  our  lifting- 
pumps  by  atmospheric  pressure ;  why,  then,  is  not  such  a  pump  a 
labor-saving  instrument? 

12.  If  water  is  to  be  raised  from  a  well  50  feet  deep,  how  high  must 
it  be  lifted,  and  how  long  must  the  barrel  be? 


Section  VI. 

TRANSMISSION  OP  EXTERNAL   PRESSURE. 

45.  Pressure  Transmitted  Undiminished  in  All  Direc- 
tions. 

Experiment  42.  —  Fill  the  glass  globe  and  cylinder  (Fig.  43)  with 
water,  and  thrust  the  piston  into  the  cylinder.  Jets  of  water  will  be 
thrown  not  only  from  that  aperture  a  in  the  globe  toward  which  the 
piston  moves  and  the  pressure  is  exerted,  but  from  apertures  on  all 
sides.  Furthermore,  the  streams  extend  to  equal  distances  in  every 
direction. 

It  thus  appears  that  external  pressure  is  exerted  not 
alone  upon  that  portion  of  the  liquid  that  lies  in  the 
path  of  the  force,  but  it  is  transmitted  equally  to  all 
parts  and  in  all  directions. 


48 


DYNAMICS   OF   FLUIDS. 


Experiment  43.  —  Measure  the  diameter  of  the  bore  of  each  arm 
of  the  glass  U-tube  (Fig.  44).     We  will  suppose,  for  illustration,  that 

the  diameters  are  respectively  40mm  and 
10mm;  then  the  areas  of  the  transverse 
sections  of  the  bores  will  be  402 : 102  =  16 ; 
that  is,  when  the  tube  contains  a  liquid, 
the  area  of  the  free  surface  of  the  liquid 
in  the  large  arm  will  be  16  times  as  great 
as  that  in  the  small  arm.  Pour  mercury 
into  the  tube  until  it  stands  about  lcm 
above  the  bottom  of  the  large  arm.  The 
mercury  stands  at  the  same  level  in  both 
arms.  Pour  water  upon  the  mercury  in 
the  large  arm  until 
this  arm  lacks  only 
about  lcm  of  being 
full.  The  pressure  of 
the  water  causes  the 
mercury  to  rise  in  the 
small  arm,  and  to  be 
depressed  in  the  large 
arm.  Pour  water  very 
slowly  into  the  small 
arm  from  a  beaker  having  a  narrow  lip,  until  the  surfaces  of  the  water 
in  the  two  arms  are  on  the  same  level.  It  is  evident  that  the  quantity 
of  water  in  the  large  arm  is  16  times  as  great  as  that  in  the  small  arm. 
This  phenomenon  appears  paradoxical  (apparently  contrary  to  the  natu- 
ral course  of  things),  until  we  master  the  important  hydrostatic  princi- 
ple involved.  We  must  not  regard  the  body  of  mercury  as  serving  as 
a  balance  beam  between  the  two  bodies  of  water,  for  this  would  lead 
to  the  absurd  conclusion  that  a  given  mass  of  matter  may  balance  an- 
other mass  16  times  as  great.  We  may  best  understand  this  phenom- 
enfljplby  imagining  the  body  of  liquid  in  the  large  arm  to  be  divided 
into  cylindrical  columns  of  liquid  of  the  same  size  as  that  in  the  small 
arm.  There  will  evidently  be  16  such  columns.  Then  whatever 
pressure  is  exerted  on  the  mercury  by  the  water  in  the  small  arm  is 
transmitted  by  the  mercury  to  each  of  the  16  columns,  so  that  each 
column  receives  an  upward  pressure,  or  a  supporting  force  equal  to 
the  weight  of  the  water  in  the  small  arm.  This  method  of  transmit- 


Fig.  44. 


TRANSMISSION   OF   EXTERNAL   PRESSURE. 


49 


ting  pressure  is  peculiar  to  fluids.  With  solids  it  is  quite  different. 
If  the  mercury  in  our  experiment  were  a  solid  body,  it  would  require 
equal  masses  of  water  placed  upon  the  two  extremities  to  counter- 
balance each  other. 

Experiment  44.  —  Support  the  seven-in-one  apparatus  with  the 
open  end  upward,  force  the  piston  in,  and  place  on  it  a  block  of  wood 
A  (Fig.  45),  and  on  the  block  a  heavy  weight  (or  let  a  small  child 
stand  on  the  block).  Attach  one  end  of  the 
rubber  tube  B  (12  feet  long)  to  the  apparatus, 
and  insert  a  tunnel  C  in  the  other  end  of  the 
tube.  Raise  the  latter  end  as  high  as  practi- 
cable, and  pour  water  into  the  tube.  Explain 
how  the  few  ounces  of  water  standing  in  the 
tube  can  exert  a  pressure  of  many  pounds  on 
the  piston,  and  cause  it  to  rise  together  with 
the  burden  that  is  on  it. 


Fig.  45.  Fig.  46. 

Experiment  45.  —  Remove  the  water  from  the  apparatus,  place  on 
the  piston  a  16-pound  weight,  and  blow  (Fig.  46)  from  the  lungs  into 
the  apparatus.  Notwithstanding  that  the  actual  pushing  force  ex- 
erted through  the  tube  by  the  lungs  does  not  probably  exceed  an 
ounce,  the  slight  increase  of  tension  caused  thereby  when  exerted 
upon  the  (about)  26  square  inches  of  surface  of  the  piston  causes  it  to 
rise  together  with  its  burden. 


A  pressure  exerted  on  a  given  area  of  a  fluid  enclosed 
in  a  vessel  is  transmitted  to  every  equal  area  of  the  inte- 
rior of  the  vessel;  and  the  whole  pressure  that  may  be 
exerted  upon  the  vessel  may  be  increased  in  proportion  as 
the  area  of  the  part  subjected  to  external  pressure  is  de- 
creased. 


50 


DYNAMICS  OF  FLUIDS. 


46.  Hydrostatic  Press.  —  This  principle  has  an  im- 
portant practical  application  in  the  hydrostatic  press. 
You  see  two  pistons  t  and  s  (Fig.  47).  The  area  of 
the  lower  surface  of  t  is  (say)  one  hundred  times  that  of 

the  lower  surface  of 
s.  As  the  piston  s  is 
raised  and  depressed, 
water  is  pumped  up 
from  the  cistern  A, 
forced  into  the  cylin- 
der a;,  and  exerts  a 
total  upward  pressure 
against  the  piston  t  one 
hundred  times  greater 
than  the  downward 
pressure  exerted  upon 
s.  Thus,  if  a  pressure 
Fig*  47*  of  one  hundred  pounds 

is  applied  at  s,  the  cotton  bales  will  be  subjected  to  a 
pressure  of  five  tons. 

The  pressure  that  may  be  exerted  by  these  presses  is  enormous.  The 
hand  of  a  child  can  break  a  strong  iron  bar.  But  observe  that,  although 
the  pressure  exerted  is  very  great,  the  upward  movement  of  the  piston  t  is 
very  slow.  In  order  that  the  piston  t  may  rise  1  inch,  the  piston  s  must  de- 
scend 100  inches.  The  disadvantage  arising  from  slowness  of  operation  is 
little  thought  of,  however,  when  we  consider  the  great  advantage  accruing 
from  the  fact  that  one  man  can  produce  as  great  a  pressure  with  the  press 
as  a  hundred  men  can  exert  without  it. 

The  press  is  used  for  compressing  cotton,  hay,  etc.,  into  bales,  and  for 
extracting  oil  from  seeds.  The  modern  engineer  finds  it  a  most  efficient 
machine,  whenever  great  weights  are  to  be  moved  through  short  distances, 
as  in  launching  ships. 


PRESSURE  EXERTED  BY  LIQUIDS. 


51 


Section  VII. 

PRESSURE  EXERTED  BY  LIQUIDS  DUE  TO  THEIR  OWN 
WEIGHT. 

47.    Pressure   Dependent  on  Depth,  but   Independ- 
ent of  the  Quantity  and  Shape  of  a  Body  of  Liquid.  — 

Having  considered  the  transmission  of  external  pressure  ap- 
plied to  any  portion  of  a  liquid,  we  proceed  to  examine  the 
effects  of  pressure  due  to  the  weight  of  liquids  themselves. 


Fig.  49. 


Fig.  50. 


Fig.  51. 


Experiment  46.  —  A  and  B  (Fig.  48)  are  two  bottomless  vessels 
which  can  be  alternately  screwed  to  a  supporting  ring  C  (Fig.  49).  The 
ring  is  itself  fastened  by  means  of  a  clamp  to  the  rim  of  a  wooden  water- 
pail.  A  circular  disk  of  metal,  D,  is  supported  by  a  rod  connected  with 
one  arm  of  the  balance-beam  E.  When  the  weight  F  is  applied  to  the 
other  arm  of  the  beam,  the  disk  D  is  drawn  up  against  the  ring  so  as 
to  supply  a  bottom  for  the  vessel  above.  Take  first  the  vessel  A, 
screw  it  to  the  ring,  and  apply  the  weight  to  the  beam  as  in  Figure  50. 
Pour  water  slowly  into  the  vessel,  moving  the  index  a  up  the  rod  so 


52  DYNAMICS   OF   FLUIDS. 

as  to  keep  it  just  at  the  surface  of  the  water,  until  the  downward 
pressure  of  the  water  upon  the  bottom  tilts  the  beam,  and  pushes  the 
bottom  down  from  the  ring,  and  allows  some  of  the  water  to  fall  into 
the  pail.  Remove  vessel  A,  and  attach  B  to  the  ring  as  in  Figure  51. 
Pour  water  as  before  into  vessel  B ;  when  the  surface  of  the  water 
reaches  the  index  a,  the  bottom  is  forced  off  as  before.  That  is,  at  the 
same  depth,  though  fa  quantity  of  water  and  the  shape  of  the  vessel  be  dif- 
ferent, the  pressure  vpon  the  bottom  of  a  vessel  is  the  same,  provided  the 
bottom  is  of  the  same  area. 

48.    Rules  for  Calculating  Liquid  Pressure  against 
the  Bottom  and  Sides  of   a  Containing  Vessel.  —  The 

pressure  due  to  gravity  on  any  portion  of  the  bottom  of  a  ves- 
sel containing  a  liquid  is  equal  to  the  weight  of  a  column  of 
the  same  liquid  whose  base  is  the  area  of  that  portion  of  the 
bottom  pressed  upon,  and  whose  hight  is  the  greatest  depth 
of  the  water  in  the  vessel.  Thus,  suppose  that  we  have 
three  vessels  having  bottoms  of  the  same  size  :  one  of 
them  has  flaring  sides,  like  a  wash-basin ;  another  has 
cylindrical  sides;  and  the  third  has  conical  sides,  like  a 
coffee-pot.  If  the  three  vessels  are  filled  with  water  to 
the  same  depth,  the  pressure  upon  the  bottom  of  each  will 
be  equal  to  the  weight  of  the  water  in  the  vessel  of  cylin- 
drical shape.  Suppose  that  the  area  of  the  bottom  of 
each  is  108  square  inches,  and  the  depth  of  water  is  16 
inches  ;  then  the  cubical  contents  of  the  water  in  the  cylin- 
drical vessel  is  1,728  cubic  inches,  or  1  cubic  foot.  The 
weight  of  1  cubic  foot  of  water  is  62|  pounds.  Hence, 
the  pressure  upon  the  bottom  of  each  vessel  is  62£  pounds. 
Evidently,  the  lateral  pressure  at  any  point  of  the  side 
of  a  vessel  depends  upon  the  depth  of  that  point;  and,  as 
depth  at  different  points  of  a  side  varies,  hence,  to  find  the 
pressure  upon  any  portion  of  a  side  of  a  vessel,  we  find  the 
weight  of  a  column  of  liquid  whose  base  is  the  area  of  that 
portion  of  the  side,  and  whose  hight  is  the  average  depth  of 
that  portion. 


PRESSURE  EXERTED  BY  LIQUIDS. 


53 


49.  The  Surface  of  a  Liquid  at  Best  is  Level.  —  This 
fact  is  commonly  expressed  thus:  "Water  always  seeks 
its  lowest  level."  In  accordance  with  this  principle,  water 
flows  down  an  inclined  plane,  and  will  not  remain  heaped 
up.  An  illustration  of  the  application  of  this  principle,  on 
a  large  scale,  is  found  in  the  method  of  supplying  cities 
with  water.  Figure  52  represents  a  modern  aqueduct, 
through  which  water  is  conveyed  from  an  elevated  pond 
or  river  #,  beneath  a  river  £>,  over  a  hill  £,  through  a  valley 


Fig.  53. 

c?,  to  a  reservoir  e,  in  a  city,  from  which  water  is  distribu- 
ted by  service-pipes  to  the  dwellings.  The  pipe  is  tapped 
at  different  points,  and  fountains  at  these  points  would 
rise  to  the  level  of  the  water  in  the  pond,  but  for  the  re- 
sistance of  the  air,  friction  in  the  pipes,  and  the  check 
which  the  ascending  steam  receives  from  the  falling  drops. 
Where  should  the  pipes  be  made  stronger,  on  a  hill 
or  in  a  valley?  Where  will  water  issue  from  faucets 
with  greater  force,  in  a  chamber  or  in  a  basement?  How 
high  may  water  be  drawn  from  the  pipe  in  the  house  /? 


54 


DYNAMICS   OF  FLUIDS. 


Section  VIII. 

THE   SIPHON. 

SO.    Construction  and  Operation  of  the  Siphon.  — •  A 

siphon  is  an  instrument  used  for  transferring  a  liquid  from 
one  vessel  to  another  through  the  agency  of  atmospheric 
pressure.  It  consists  of  a  tube  of  any  material  (rubber  is 
often  most  convenient)  bent  into  a  shape  somewhat  like 
the  letter  U.  To  set  it  in  operation,  fill  the 
tube  with  a  liquid,  stop  each  end  with  a 
finger  or  cork,  place  it  in  the  position  rep- 
resented in  Figure  53,  remove  the  stoppers 
and  the  liquid  will  all  flow  out  at  the  orifice 
o.  Why?  The  upward  pressure  of  the  at- 
mosphere against  the  liquid  in  the  tube  is 
the  same  at  both  ends ;  hence  these  two 
forces  are  in  equilibrium.  But  the  weight 
of  the  column  of  liquid  ab  is  greater  than 
the  weight  of  the  column  do ;  hence  equilibrium  is  de- 
stroyed and  the  movement  is  in  the  direction  of  the  greater 
(i.e.  the  unbalanced)  force.  The  unbalanced  force  which 
causes  the  flow  is  equal  to  the  weight  of  the  column  eb. 

If  one  end  of  the  tube  filled  with  liquid  is  immersed  in 
a  liquid  in  some  vessel,  as  in  A,  Figure  54,  and  the  other 
end  is  brought  below  the  surface  of  the  liquid  in  the  vessel 
and  the  stoppers  are  removed,  the  liquid  in  the  vessel  will 
flow  out  through  the  tube  until  the  distance  eb  becomes 
zero. 


Fig.  53. 


If  one  0f  the  vessels  is  raised  a  little,  as  in  C,  the  liquid  will  flow  from 
the  raised  vessel,  till  the  surfaces  in  the  two  vessels  are  on  the  same  leveL 


THE   SIPHON. 


55 


The  remaining  diagrams  in  this  cut  represent  some  of  the  great  variety  of 
uses  to  which  the  siphon  may  be  put.  D,  E,  and  F  are  different  forms  of 
siphon  fountains.  In  D,  the  siphon  tube  is  filled  by  blowing  in  the  tube  /. 
Explain  the  remainder  of  the  operation.  A  siphon  of  the  form  G  is  always 
ready  for  use.  It  is  only  necessary  to  dip  one  end  into  the  liquid  to  be 


Fig.  54. 

transferred.  Why  does  the  liquid  not  flow  out  of  this  tube  in  its  present 
condition?  H  illustrates  the  method  by  which  a  heavy  liquid  may  be 
removed  from  beneath  a  lighter  liquid.  By  means  of  a  siphon  a  liquid 
may  be  removed  from  a  vessel  in  a  clear  state,  without  disturbing  sediment 


56 


DYNAMICS   OF  FLUIDS. 


at  the  bottom.  I  is  a  Tantalus  Cup.  A  liquid  will  not  flow  from  this  cup 
till  the  top  of  the  bend  of  the  tube  is  covered.  It  will  then  continue  to  flow 
as  long  as  the  end  of  the  tube  is  in  the  liquid.  The  cup  g  (Fig.  34,  page 
42)  is  a  Tantalus  cup.  The  siphon  J  may  be  filled  with  a  liquid  that  is 
not  safe  or  pleasant  to  handle,  by  placing  the  end  j  in  the  liquid,  stopping 
the  end  k,  and  sucking  the  air  out  at  the  end  I  till  the  lower  end  is  filled 
with  the  liquid. 

Gases  heavier  than  air  may  be  siphoned  like  liquids.  Vessel  o  contains 
carbonic-acid  gas.  As  the  gas  is  siphoned  into  the  vessel  p,  it  extinguishes 
a  candle-flame.  Gases  lighter  than  air  are  siphoned  by  inverting  both  the 
vessels  and  the  siphon. 


Section  IX. 


BUOYANT   FOECE  OF  FLUIDS. 

51.    Origin  of  Buoyancy. 

Experiment  47.  —  Gradually  lower  a  large  stone,  by  a  string  tied 
to  it,  into  a  bucket  of  water,  and  notice  that 
its  weight  gradually  becomes  less  till  it  is  com- 
pletely submerged.  Slowly  raise  it  out  of  the 
water,  and  note  the  change  in  weight  as  it  emerges 
from  the  water.  Suspend  the  stone  from  a  spring 
balance,  weigh  it  in  air  and  then  in  water,  and 
ascertain  its  loss  of  weight  in  the  latter. 

It  seems  as  if  something  in  the  fluid, 
underneath  the  articles  submerged,  were 
pressing  up  against  them.  A  moment's  re- 
flection will  make  the  explanation  of  this 
phenomenon  apparent.  We  have  learned  (1)  that  pressure 
at  any  given  point  in  a  body  of  fluid  is  equal  in  all  direc- 
tions. (2)  That  pressure  in  liquids  increases  as  the 


Fig.  55. 


BUOYANT   FORCE   OF    FLUIDS. 


57 


depth.  Consequently,  the  downward  pressure  on  the  top 
(i.e.  the  place  of  least  depth)  of  a  body  immersed  in  a 
fluid,  as  dcba  (Fig.  55),  must  be  less  than  the  upward 
pressure  against  the  bottom;  hence,  there  is  an  unbal- 
anced force  acting  upward,  which  tends  to  neutralize  to 
some  extent  the  weight  or  gravity  of  the  body.  This 
unbalanced  force  is  called  the  buoyant  force  of  fluids. 
That  there  is  equilibrium  between  the  pressures  on  the 
sides  of  a  body  immersed  is  shown  by  the  fact  that  there 
is  no  tendency  to  move  laterally. 


52.    Magnitude  of  the  Buoyant  Force. 

Experiment  48.  —  Suspend  from  one  arm  of  a  balance  beam  a 
cylindrical  bucket  A  (Fig.  56),  and  from  the  bucket  a  solid  cylinder 
whose  volume  is    exactly  equal  to  the 
capacity  of  the  bucket;  in  other  words, 
the   latte-r  would   just    fill    the    former. 
Counterpoise  the    bucket    and    cylinder 
with  weights. 

Place  beneath  the  cylinder  a  tumbler  of 
water,  and  raise  the  tumbler  until  the  cyl- 
inder is  completely  submerged.  The 
buoyant  force  of  the  water  destroys  the 
equilibrium.  Pour  water  into  the  bucket ; 
when  it  becomes  just  even  full,  the  equi- 
librium is  restored. 

Now  it  is  evident  that  the  cylinder 
immersed  in  the  water  displaces  its  own 
volume  of  water,  or  just  as  much  water 
as  fills  the  bucket.  But  the  bucket  full 
of  water  is  just  sufficient  to  restore  the  weight  lost  by  the  submersion 
of  the  cylinder.  Hence,  a  solid  immersed  in  a  liquid  is  buoyed  up  with  a 
force  equal  to  (i.e.  its  apparent  loss  in  weight  is)  the  weight  of  the 
liquid  it  displaces. 

Experiment  49.  —  The  last  statement  maybe  verified  in  another 
way  with  apparatus  like  tharl  shown  in  Figure  57.  Fill  the  vessel  A 
till  the  liquid  overflows  at  E.  After  the  overflow  ceases,  place  a  ves- 


Fig.  56. 


58 


DYNAMICS   OF  FLUIDS. 


sel  c  under  the  nozzle.    Suspend  a  stone  from  the  balance-beam  B, 
and  weigh   it  in  air,  and  then   carefully  lower  it  into  the  liquid, 

when  some  of  the  liquid 
will  flow  into  the  vessel  c. 
The  vessel  c  having  been 
weighed  when  empty,  weigh 
it  again  with  its  liquid 
contents,  and  it  will  be 
found  that  its  increase  in 
weight  is  just  equal  to  the 
loss  of  weight  of  the  stone. 
Experiment  50.  —  Next 
suspend  a  block  of  wood 
that  will  float  in  the  liquid, 
and  weigh  it  in  air.  Then 
float  it  upon  the  liquid,  and 
weigh  the  liquid  displaced  as 
before,  and  it  will  be  found 
that  the  weight  of  the  liquid 
Fig.  57.  displaced  is  just  equal  to  the 

weight  of  the  block  in  air. 

Hence,  a  floating  body  displaces  its  own  weight  of  liquid  ; 
in  other  words,  a  floating  body  will  sink  till  it  displaces  an 
equal  weight  of  the  liquid,  or  till  it  reaches  a  depth  where 
the  buoyant  force  is  equal  to  its  own  weight. 


Experiment  51.  —  Place  a  baroscope  (Fig.  58), 
consisting  of  a  scale-beam,  a  small  weight,  and  a 
hollow  brass  sphere,  under  the  receiver  of  an  air- 
pump,  and  exhaust  the  air.  In  the  air  the  weight 
and  sphere  balance  each  other;  but  when  the 
air  is  removed,  the  sphere  sinks,  showing  that  in 
reality  it  is  heavier  than  the  weight.  In  the  air 
each  is  buoyed  up  by  the  weight  of  the  air  it  dis- 
places ;  but  as  the  sphere  displaces  more  air,  it  is 
buoyed  up  more.  Consequently,  when  the  buoyant 
force  is  withdrawn  from  both,  their  equilibrium 
is  destroyed. 


58. 


DENSITY  AND   SPECIFIC   GRAVITY. 


59 


We  see  from  this  experiment  that  bodies  weigh  less  in 
air  than  in  a  vacuum,  and  that  we  never  ascertain  the  true 
weight  of  a  body,  except  when  weighed  in  a  vacuum. 

The  density  of  the  atmosphere  is  greatest  at  the  surface 
of  the  earth.  A  body  free  to  move  cannot  displace  more 
than  its  own  weight  of  a  fluid  ;  therefore  a  balloon,  which 
is  a  large  bag  filled  with  a  gas  about  fourteen  times  lighter 
than  air  at  the  sea-level,  will  rise  till  the  balloon,  plus  the 
weight  of  the  car  and  cargo,  equals  the  weight  of  the  air 
displaced. 

Figure  59  represents  a  water-tank  in  common  use  in  our  houses.  Water 
enters  it  from  the  main 
until  nearly  full,  when  it 
reaches  the  hollow  metallic 
ball  A,  and  raises  it  by  its 
buoyant  force  and  closes  a 
valve  in  the  main  pipe,  and 
thus  prevents  an  overflow. 
An  overflow  is  still  further 
prevented  by  the  waste 
pipe  and  another  "ball 
tap,"  B,  which  opens  at 
a  suitable  time  another 
passage  for  the  escape  of 
water. 


Fig.  59. 


Section  X. 

DENSITY  AND  SPECIFIC  GRAVITY. 

53.  Meaning  of  the  Terms  and  their  Relation  to 
each  Other.  —  The  quantity  of  matter  per  unit  of  volume 
represents  the  density  of  the  matter  filling  that  space. 


60  DYNAMICS   OF   FLUIDS. 

Thus,  a  gram  of  water  at  4°  C.  (centigrade  thermometer) 
occupies  a  cubic  centimeter ;  while  the  same  space  would 
contain  11.5  grams  of  lead.  Every  kind  of  matter  (i.e. 
every  substance)  has  a  special  or  specific  density  of  its 
own.  Pure  water  at  4°  C.  is  taken  as  a  standard  ;  and  its 

density  is   said   to  be  (  mass    =  ¥- =\I.     In  the  same 
\volume      lcc      / 

way  the  density  of  lead  is  ( — 1-^-  =  )  11.5.    A  piece  of  lead 

which  occupies  a  given  space  not  only  contains  11.5  times 
as  much  matter,  but  also  weighs  11.5  times  as  much  as  the 
quantity  of  water  which  would  fill  the  same  space.  The 
density  of  any  liquid  or  solid  compared  with  that  of  water 
is  a  ratio  — called  its  specific  density ;  this  ratio  is  numeri- 
cally equal  to  the  ratio,  called  its  specific  gravity,  of  its 
weight  compared  with  the  weight  of  an  equal  volume  of 
water  at  the  standard  temperature. 

54.  Formulas  for  Specific  Density  and  Specific  Grav- 
ity.—  Let  D  represent  the  density  of  any  given  substance 
(e.g.  lead),  and  D  the  density  of  water,  and  let  G  and  G' 
represent  respectively  the  weights  of  equal  volumes  of  the 
same  substances ;  then 

x.j  x   Density  of  given  substance  _  D «     ^ 

Density  of  water  =  D7  ~ 

Weight  of  a  given  volume  of  the  substance  _  G g    ^ 

Weight  of  equal  volume  of  water  G' 

The  Sp.  D.  of  lead  =  ~  =  ^  =  11.5.      The  Sp.  G.  of 
^?=lH«ilA      Hence  Sp.  D.   and   Sp.  G.  are 

numerically  equal.  In  the  same  way  ratios  may  be  found  for 
other  substances  and  recorded  in  a  table ;  such  a  table  ex- 
hibits both  the  specific  densities  and  the  specific  gravities 
of  the  substances.  See  Appendix  B. 


SPECIFIC  GRAVITY  AND  SPECIFIC  DENSITY. 


61 


Section  XI. 

EXPERIMENTAL  METHODS   OF   FINDING  THE  SPECIFIC 
DENSITY   AND   SPECIFIC   GRAVITY   OF  BODIES. 

55.    Solids. 

Experiment  52.  —  From  a  hook  beneath  a  scale-pan  (Fig.  60) 
suspend  by  a  fine  thread  a  small  specimen  of  a  substance  whose 
specific  gravity  is  to  be  found,  and  weigh  it,  while  dry,  in  the  air.  Then 
immerse  the  body  in  a  tumbler  of  water  (do  not  allow  it  to  touch  the 
tumbler,  and  see  that  it  is  completely  submerged),  and  weigh  it  in 
water.  The  loss  of  weight  in  water  is  evidently  G ',  i.e.  the  weight 
of  the  water  displaced  by  the  body ;  or,  in  other  words,  the  weight 
of  a  body  of  water  having  the  same  volume  as  that  of  the  specimen. 
Apply  the  formula  (2)  for  finding  the  specific  gravity. 


Fig.  60. 


Fig.  61. 


Experiment  53.  —  Take  a  piece  of  sheet  lead  one  inch  long  and 
one-half  inch  wide,  weigh  it  in  air  and  then  in  water,  and  find  its  loss 
of  weight  in  water.  [It  will  not  be  necessary  to  repeat  this  part  of 
the  operation  in  future  experiments.]  Weigh  in  air  a  piece  of  cork 
or  other  substance  that  floats  in  water,  then  fold  the  lead-sinker,  and 
place  it  astride  the  string  just  above  the  specimen,  completely  immerse 
both,  and  find  their  combined  weight  in  water.  Subtract  their  com- 
bined weight  in  water  from  the  sum  of  the  weights  of  both  in  air ; 
this  gives  the  weight  of  water  displaced  by  both.  Subtract  from  this 


62 


DYNAMICS   OF  FLUIDS. 


the  weight  lost  by  the  lead  alone,  and  the  remainder  is  G7 ;  i~e.  the 
weight  of  water  displaced  by  the  cork.    Apply  formula  (2),  as  before. 

56.    Liquids. 

Experiment  54.  —  Take  a  specific-gravity  bottle  that  holds  when 
filled  a  certain  (round)  number  of  grams  of  water,  e.g.  100s,  200s,  etc. 
Fill  the  bottle  with  the  liquid  whose  specific  gravity  is  sought.  Place 
it  on  a  scale-pan  (Fig.  61),  and  on  the  other  scale-pan  place  a  piece  of 
metal  a,  which  is  an  exact  counterpoise  for  the  bottle  when  empty. 
On  the  same  pan  place  weights  b,  until  there  is  equilibrium.  The 
weights  placed  in  this  pan  represent  the  weight  W  of  the  liquid  in  the 
bottle.  Apply  formula  (2).  The  W  (i.e.  the  100&,  200&,  etc.)  is  the 
same  in  every  experiment,  and  is  usually  etched  on  the  bottle. 

Experiment  55.  —  Take  a  pebble  stone  (e.g.  quartz)  about  the 
size  of  a  large  chestnut,  find  its  loss  of  weight  (i.e.  W)  in  water ;  find 
its  loss  of  weight  (i.e.  W)  in  the  given  liquid.  Apply  formula  (2). 

Prepare  blanks,  and  tabulate  the  results  of  the  experiments  above 
as  follows :  — 


NAME  OF  SUBSTANCE. 

W  in 

Grams. 

W  in 
Grams. 

Sp.  G. 
or 
Sp.  D. 

E. 

Lead        .... 

7.2 

6.6 

12 

.5 

When  the  result  obtained  differs  from  that  given  in  the  table  of 
specific  gravities  (see  Appendix  B),  the  difference  is  recorded  in  the 
column  of  errors  (e).  The  results  recorded  in  the  column  of  errors 
are  not  necessarily  real  errors ;  they  may  indicate  the  degree  of  im- 
purity, or  some  peculiar  physical  condition,  of  the  specimen  tested. 

57.  Hydrometers.  —  If  a  wooden,  an  iron,  and  a  lead 
ball  are  placed  in  a  vessel  containing  mercury  (Fig.  62), 


SPECIFIC   GEAVITY  AND  SPECIFIC  DENSITY. 


63 


they  will  float  on  the  mercury  at  different  depths,  accord- 
ing to  their  relative  densities.  Ice  floats,  in  water  with 
TVfr%,  in  mercury  with  Tffg-,  of  its  bulk  submerged.  Hence 
the  Sp.  D.  of  mercury  is  918  -*-  60  =  about  13.5. 

We  see,  then,  that  the  densities  of  liquids  may  be  com- 
pared by  seeing  to  what  depths  bodies  floating  in  them 
will  sink.  An  instrument  (A,  Fig.  63)  called  a  hydrometer 
is  constructed  on  this  principle.  It  consists  of  a  glass 
tube  with  one  or  more  bulbs  blown  in  it,  loaded  at  one 
end  with  shot  or  mercury  to  keep  it  in  a  vertical  position 
when  placed  in  a  liquid.  It  has  a  scale  of  specific  densities 
on  the  stem,  so  that  the  experimenter  has  only  to  place  it 
in  the  liquid  to  be  tested,  and  read  its  specific  density  or 
specific  gravity  at  that  point,  B,  of  the  stem  which  is  at 
the  surface  of  the  liquid. 


Fig. 


Fig.  63. 


58.   Miscellaneous  Experiments. 

Experiment  56.  —  Find  the  cubical  contents  of  an  irregular  shaped 
body,  e.g.  a  stone.  Find  its  loss  of  weight  in  water.  Remember  that 
the  loss  of  weight  is  precisely  the  weight  of  the  water  it  displaces,  and 
that  the  volume  of  one  gram  of  water  is  one  cubic  centimeter. 


64  DYNAMICS   OF   FLUIDS. 

Experiment  57.  —  Find  the  capacity  of  a  test-tube,  or  an  irregular 
shaped  cavity  in  any  body.  Weigh  the  body ;  then  fill  the  cavity  with 
water,  and  weigh  again.  As  many  grams  as  its  weight  is  increased,  so 
many  cubic  centimeters  is  the  capacity  of  the  cavity. 

Experiment  58.  —  A  fresh  egg  sinks  in  water.  See  if  by  dissolv- 
ing table  salt  in  the  water  it  can  be  made  to  float.  How  does  salt 
affect  the  density  of  the  water? 

Experiment  59.  —  Float  a  sensitive  hydrometer  in  water  at  about 
60°  F.  (15°  C.),  and  in  other  water  at  about  180°  F.  (82°  C.).  Which 
water  is  denser  ? 

EXERCISES. 

1.  In  which  does  a  liquid  stand  higher,  in  the  snout  of  a  coffee-pot 
or  in  the  main  body?    On  which  does  this  show  that  pressure  depends, 
on  quantity  or  depth  of  liquid  ? 

2.  The  areas  of  the  bottoms  of  vessels  A,  B,  and  C  (Fig.  64)  are  equal. 
The  vessels  have  the  same  depth,  and  are  filled  with  water.    Which 
vessel  contains  the  more  water  ?    On  the  bottom  of  which  vessel  is  the 
pressure  equal  to  the  weight  of  the  water  which  it  contains  ?    How 
does  the  pressure  upon   the  bottom  of  vessel  B  compare  with  the 
weight  of  the  water  in  it? 


Fig.  64. 

3.  A  cubic  foot  of  water  weighs  about  62.5  pounds  or  1,000  ounces. 
Suppose  that  the  area  of  the  bottom  of  each  vessel  is  50  square  inches 
and  the  depth  is  10  inches ;   what  is  the  pressure  on  the  bottom  of 
each? 

4.  Suppose  that  the  vessel  A  is  a  cubical  vessel ;  what  is  the  pres- 
sure against  one  of  its  vertical  sides  ? 

5.  Suppose  that  vessel  A  were  tightly  covered,  and  that  a  tube  10 
feet  long  were  passed  through  a  perforation  in  the  cover  so  that  the  end 
just  touches  the  upper  surface  of  the  water  in  the  vessel ;  then  sup- 
pose the  tube  to  be  filled  with  water.     If  the  area  of  the  cross-section 


SPECIFIC   GRAVITY   AND   SPECIFIC   DENSITY. 


65 


of  the  bore  is  1  square  inch,  what  additional  pressure  will  each  side  of 
the  cube  sustain? 

6.  Suppose  that  the  area  of  the  end  of  the  large  piston  of  a  hydro- 
static press  is  100  square  inches ;  what  should  be  the  area  of  the  end 
of  the  small  piston  that  a  force  of  100  pounds  applied  to  it  may  produce 
a  pressure  of  2  tons  ? 

7.  A  solid  body  weighs  10  pounds  in  air  and  6  pounds  in  water,   (a) 
What  is  the  weight  of  an  equal  bulk  of  water  ?     (b)  What  is  its  specific 
-gravity?     (c)  What  is  the  volume  of  the  body?     (d)  What  would  it 
weigh  if  it  were  immersed  in  sulphuric  acid?    [See  table  of  specific 
gravities,  Appendix  B.] 

8.  A  thousand-grain    specific-gravity  bottle  filled  with  sea-water 
requires  in  addition  to  the  counterpoise  of  the  bottle  1,026  grains  to 
balance  it.     (a)  What  is  the  specific  gravity  of  sea-water  ?     (6)  What 
is  the  quantity  of  salt,  etc.,  dissolved  in  1,000  grams  of  sea-water? 

9.  A  piece  of  cork  floating  on  water  displaces  2  pounds  of  water. 
What  is  the  weight  of  the  cork? 

10.  In  which  would  a  hydrometer  sink  farther,  in  milk  or  water? 

11.  What  metals  will  float  in  mercury? 

12.  (a)  Which  has  the  greater  specific  gravity,  water  at  10°  C.  or 
water  at  20°  C.?     (&)  If  water  at  the  bottom  of  a  vessel  could  be 
raised  by  application  of  heat  to  20  °  C.  while  the  water  near  the  upper 
surface  has  a  temperature  of  10°  C.,  what  would  happen? 

13.  A  block  of  wood  weighs  550  grams ;   when  a  certain  irregular- 
shaped  cavity  is   filled  with  mercury  the  block  weighs   570  grams. 
What  is  the  capacity  or  cubical  contents  of  the  cavity? 

14.  In  which  is  it  easier  for  a  person  to  float,  in  fresh  water  or  in 
sea-water?    Why? 

15.  Figure  65  represents   a  beaker  graduated 
in  cubic  centimeters.     Suppose  that  when  water 
stands  in  the  graduate  at  50CC,  a  pebble  stone  is 
dropped  into  the  water,  and  the  water  rises  to 
75CC.      (a)  What  is  the   volume  of    the   stone? 
(ft)  How  much  less  does  the  stone  weigh  in  water 
than  in  air  ?    (c)  What  is  the  weight  of  an  equal 
volume  of  water  ? 

16.  If  a  piece  of  cork  is  floated  on  water  in 
a  graduate,  and  displaces  (i.e.  causes  the  water 

to  rise)  7CC,  what  is  the  weight  of  the  cork  ?  Fig.  65. 


66  DYNAMICS   OF   FLUIDS. 

17.  If  a  piece  of  lead  (sp.  g.  11.35)  is  dropped  into  a  graduate  and 
displaces  12CC  of  water,  what  does  the  lead  weigh  ?    (a)  How  would 
you  measure  out  50  grams  of  water  in  a  graduate  ?    (&)  How  would 
you  measure  out  the  same  weight  of  alcohol  (sp.  g.  0.8)  ?    (c)  How  the 
same  weight  of  sulphuric  acid  (sp.  g.  1.84)? 

18.  What  is  the  density  of  gold?  silver?  milk?  alcohol? 

19.  When  the  barometer  stands  at  30  inches,  how  high  can  alcohol 
be  raised  by  a  perfect  lifting-pump  ? 

20.  A  measuring  glass   graduated   in  cubic  centimeters   contains 
water.     An  empty  bottle  floats  on  the  water,  and  the  surface  of  the 
water  stands  at  50CC.     If  10s  of  lead  shot  are  placed  in  the  bottle, 
where  will  the  surface  of  the  water  stand? 

21.  What  evidence  do  we  see  daily  that  there  is  relative  motion 
between  the  sun  and  the  earth? 

22.  On  what  two  things  does  the  weight  of  a  body  depend  ? 

23.  (a)  Can  you  suck  air  out  of  a  bottle  ?     (6)  Can  you  suck  water 
out  of  a  bottle  ?    Explain. 

24.  (a)  What  bodies  have  neither  volume  nor  shape  ?     (J)  What 
have  volume,  but  not  shape?    (c)  What  have  both  volume  and  shape? 

25.  When  the  volume  of  a  body  of  gas  diminishes,  is  it  due  to  con- 
traction or  compression,  i.e.  to  internal  or  external  forces? 

26.  What  is  the  hight  of  the  barometer  column  when  the  atmos- 
pheric pressure  is  10  grams  per  square  centimeter  ? 

27.  A  barometer  in  a  diving-bell  (page  3)  stands  at  96cm  when  a 
barometer  at  the  surface  of  the  earth  stands  at  76cm;  what  is  the 
depth  of  the  surface  of  water  inside  the  bell  ? 


CHAPTER   III. 
GENERAL  DYNAMICS. 

Section  I. 

MOMENTUM  AND   ITS   RELATION   TO   FORCE. 

59.  Momentum.  —  An  empty  car   in   motion  is  much 
more  easily  stopped  than  a  loaded   car  moving  with  the 
same  speed.     Evidently,  if  force  is  employed  to  destroy 
motion,  and  it  takes  either  a  greater  force  to  stop  the 
loaded   car  in  a  given  time,  or   the  same  force  a  longer 
time,  it   follows   that  there   must   be    more   motion  to  be 
destroyed  in  the  loaded  car  than  in  the  empty  car  mov- 
ing with  the  same  velocity.     Quantity  of   motion,  more 
briefly  momentum,  and  velocity  are  not  identical.     Momen- 
tum  depends   upon  both   mass   and  velocity,   velocity  is 
independent  of  mass.     Momentum  =  MV. 

The  momentum  of  a  moving  body  is  measured  by  the  prod- 
uct of  its  mass  multiplied  by  its  velocity. 

60.  Relation  of  Momentum  to  Force. 

Experiment  60.  —  Weights  A  and  B  of  the  Atwood  machine 
(Fig.  66),  suspended  by  a  thread  passing  over  the  wheel  C,  are  in 
equilibrium  with  reference  to  the  force  of  gravity ;  consequently  neither 
falls.  Raise  weight  A,  and  let  it  rest  on  the  platform  D,  as  in  Figure 
67.  The  two  weights  are  still  in  equilibrium.  Place  weight  E,  called 
a  "  rider,"  on  A.  There  is  now  an  unbalanced  force,  and  if  the  plat- 
form D  is  removed,  there  will  be  motion,  i.e.  A  and  E  will  fall,  and 
B  will  rise.  Set  the  pendulum  F  to  vibrating.  At  each  vibration  it 


68 


GENERAL  DYNAMICS. 


Fig.  66. 


causes  a  stroke  of  the  hammer  on  the  bell  G. 
At  the  instant  of  the  first  stroke  the  pendulum 
causes  the  platform  D  to  drop  so  as  to  allow 
the  weights  to  move.  When  the  weights  reach 
the  ring  H,  the  rider  is  caught  off  by  the  ring. 

Raise  and  lower  the  ring  on  the  graduated 
pillar  I,  and  ascertain  by  repeated  trials  the 
average  distance  the  weights  descend  in  the  in- 
terval between  the  first  two  strokes  of  the  bell. 

Next  substitute  for  E  a  weight  L,  double  that 
of  E.  Find  by  trial  how  far  the  weights  now 
descend  in  the  same  interval  of  time  as  before. 
It  will  be  found  that  in  the  latter  case  the 
weights  descend  nearly  twice  as  far  as  in  the 
first  case. 

Suppose  that  weights  A  and  B  are  each  30 
grams,  and  that  weights  E  and  L  are  respec- 
tively 2  grams  and  4  grams.  Now  the  force  of 
gravity  which  acts  on  weight  E  is  2  grains. 
Consequently  the  unbalanced  force  which  put 
in  motion  the  three  weights  A,  B,  and  E,  whose 
combined  weight  (disregarding  the  weight  of 
wheel  C,  which  is  also  put  in  motion)  is 
(30  +  30  +  2  =  )  62  grams,  was  2  grams.  It 
is  now  evident  why  the  descent  is  slow,  for  in- 
stead of  a  force  of  1  gram  acting  upon  each  gram 
of  matter,  as  is  usually  the  case  with  falling 
bodies,  we  have  a  force  of  only  2  grams  moving 
62  grams  of  matter ;  consequently  the  descent 
is  about  j\  as  fast  as  that  of  falling  bodies 
generally. 

But  when  we  employed  weight  L,  we  had  a 
force  of  4  grams  moving  (30  +  30  +  4  =)  64 
grams  of  matter.  Here  the  force  is  doubled, 
and  the  distance  traversed  is  nearly  doubled; 
consequently  the  average  velocity  and  the  mo- 
mentum acquired  are  nearly  doubled.  Had  the 
masses  moved  in  the  two  cases  been  exactly  the 
same,  the  velocity  and  the  momentum  would 
have  been  exactlv  doubled. 


FIRST   LAW   OF   MOTION. 


69 


(1)  In  equal  intervals  of  time  change  of  momentum  is 
proportional  to  the  force  employed. 

Experiment  61.  —  Once  more  place  E  on 
A,  and  ascertain  how  far  they  will  descend 
between  the  first  and  third  strokes  of  the 
bell,  i.e.  in  double  the  time  employed  before. 
It  will  be  found  that  they  will  descend  in 
the  two  units  of  time  about  four  times  as 
far  as  during  the  first  unit  of  time.  Later 
on  it  will  be  shown  that,  in  order  to  accom- 
plish this,  the  average  velocity  during  the 
second  unit  of  time  must  be  twice  that  dur- 
ing the  first  unit  of  time.  If  MV  represent 
the  momentum  generated  during  the  first 
unit  of  time,  then  the  momentum  generated 
during  the  second  unit  of  time  must  be  about 
2MV. 

(2)  The  momentum  generated  by  a 

given  force  is  proportional  to  the  time  during  which  the  force 
acts. 


Section  II. 

FIRST   LAW    OF   MOTION. 

The  relations  between  matter  and  force  are  concisely 
expressed  in  what  are  known  as  The  Three  Laws  of 
Motion  first  enunciated  by  Sir  Isaac  Newton. 

61.  First  Law  of  Motion.  —  A  body  at  rest  remains  at 
rest,  and  a  body  in  motion  moves  with  uniform  velocity  in  a 
straight  line,  unless  acted  upon  by  some  external  force. 

That  part  of  the  law  which  pertains  to  motion  is  briefly 


70  GENERAL  DYNAMICS. 

summarized  in  the  familiar  expression,  "  perpetual  motion." 
"Is  perpetual  motion  possible?"  has  been  often  asked. 
The  answer  is  simple,  —  Yes,  more  than  possible,  neces- 
sary, if  no  force  interferes  to  prevent.  What  has  a  person 
to  do  who  would  establish  perpetual  motion?  Isolate  a 
moving  body  from  interference  of  all  external  forces,  such 
as  gravity,  friction,  and  resistance  of  the  air.  Can  the  con- 
dition be  fulfilled? 

In  consequence  of  its  utter  inability  to  put  itself  in  motion  or  to  stop 
itself,  every  body  of  matter  tends  to  remain  in  the  state  that  it  is  in  with 
reference  to  motion  or  rest ;  this  inability  is  called  inertia.  The  First  Law 
of  Motion  is  often  appropriately  called  the  Law  of  Inertia. 


Section  III. 

SECOND    LAW    OF   MOTION. 

62.    Graphical  Representation  of  Motion  and  Force. 

—  If  a  person  wishes  to  describe  to  you  the  motion  of 
a  ball  struck  by  a  bat,  he  must  tell  you  three  things : 
(1)  where  it  starts,  (2)  in  what  direction  it  moves,  and 
(3)  how  far  it  goes.  These  three  essential  elements  may 

be    represented    graphically   by 
lines.     Thus,  suppose  balls  at  A 
and  D   (Fig.  68)   to  be  struck 
by  bats,  and  that  they  move  re- 
rig.  68.  spectively   to   B   and  E  in  one 
second.     Then  the   points  A  and  D   are   their   starting- 
points  ;   the  lines  AB  and  DE  represent  the  direction  of 
their  motions,  and  the  lengths  of  the  lines  represent  the 


/y; 

SECOND   LAW   OF  MOTION.  71 

distances  traversed.  In  reading,  the  direction  should  be 
indicated  by  the  order  of  the  letters,  as  AB  and  DE. 

Likewise,  the  forces  which  produce  the  motion  may  be 
represented  graphically.  For  example,  the  points  A  and 
B  may  represent  the  points  where  the  forces  begin  to  act, 
the  lines  AB  and  DE  represent  the  direction  in  which  they 
act,  and  the  length  of  the  lines  represent  their  relative 
intensities. 

Let  a  force  whose  intensity  may  be  represented  numeri- 
cally by  8  (e.g.  8  pounds),  acting  in  the  direction  AB  (Fig. 
69),  be  applied  continuously  to 
a  ball  starting  at  A,  and  sup- 
pose this  force  capable  of  mov- 
ing it  to  B  in  one  second ;  now, 
at  the  end  of  the  second  let 
a  force  of  the  intensity  of  4, 
directed  at  right  angles  to  the 
direction  of  the  former  force, 
act  during  a  second  —  it  would  Fig.  69. 

move  the  ball  to  C.  If,  however,  when  the  ball  is  at  A, 
both  of  these  forces  should  be  applied  at  the  same  time,  then 
at  the  end  of  a  second  the  ball  will  be  found  at  C.  Its 
path  will  not  be  AB  nor  AD,  but  an  intermediate  one, 
AC.  Still  each  force  produces  its  own  peculiar  result,  for 
neither  alone  would  carry  it  to  C,  but  both  are  required. 

63.  Second  Law  of  Motion.  —  Change  of  momentum  is 
in  the  direction  in  which  the  force  acts,  and  is  proportional 
to  its  intensity  and  the  time  during  which  it  acts. 

This  law  implies  that  an  unbalanced  force  of  the  same 
intensity,  in  the  same  time,  always  produces  exactly  the 
same  change  of  momentum,  regardless  of  the  mass  of  the 
body  on  which  it  acts,  and  regardless  of  whether  the  body  is 
in  motion  or  at  rest,  and  whether  the  force  acts  alone  or  with 
others  at  the  same  time. 


72  GENERAL  DYNAMICS. 

Section  IV. 

COMPOSITION   AND   RESOLUTION   OF   FORCES. 

64.    Composition  of  Forces.  —  It  is  evident  that  a  sin- 
gle force,  applied  in  the  direction  AC  (Fig.  69),  might 
produce    the   same  result   that   is   produced   by  the   two 
forces  represented  by  AB  and  AD.     Such  a  force  is  called 
a  resultant.    A  resultant  is  a  single  force  that  may  be  sub- 
stituted for  two  or  more  forces, 
and  produce  the  same  result 
that   the   simultaneous   action 
of  the  combined  forces  produce. 
The  several  forces  that  con- 
tribute to  produce  the  result- 
ant are  called  its  components. 
When    the    components   are 
given,  and  the  resultant  re- 
quired, the  problem  is  called 

composition  of  forces.  The  resultant  of  two  forces  acting 
simultaneously  at  an  angle  to  each  other  may  always  be 
represented  by  a  diagonal  of  a  parallelogram,  of  which  the 
two  adjacent  sides  represent  the  components.  Thus,  the 
lines  AD  and  AB  represent  respectively  the  direction  and 
relative  intensity  of  each  component,  and  AC  represents 
the  direction  and  intensity  of  the  resultant. 

The  numerical  value  of  the  resultant  may  be  found  by 
comparing  the  length  of  the  line  AC  with  the  length  of 
either  AB  or  AD,  whose  numerical  values  are  known. 
Thus,  AC  is  2.23  times  AD;  hence,  the  numerical  value 
of  the  resultant  AC  is  (4  X  2.23  =)  8.92. 

When  more  than  two  components  are  given,  find  the  result- 


COMPOSITION  AND  EESOLUTION  OP  FORCES.  73 

ant  of  any  two  of  them,  then  of  this  resultant  and  a  third, 
and  so  on  until  every  component  has  been  used.  Thus,  in 
Fig.  70,  AC  is  the  resultant  of  AB  and  AD,  and  AF  is 
the  resultant  of  AC  and  AE,  i.e.  of  the  three  forces  AB, 
AD,  and  AE.  Generally  speaking,  a  motion  may  be  the 
result  of  any  number  of  forces.  When  we  see  a  body  in 
motion,  we  cannot  determine  by  its  behavior  how  many 
forces  have  concurred  to  produce  its  motion. 

65.  Resolution  of  Forces.  —  Assume  that  a  ball  moves 
a  certain  distance  in  a  cer- 
tain direction,  AC  (Fig. 
71),  under  the  combined 
influence  of  two  forces, 
and  that  one  of  the  forces 
that  produces  this  motion 
is  represented  in  intensity 

and  direction  by  the  line  AB :  what  must  be  the  intensity 
and  direction  of  the  other  force  ?  Since  AC  is  the  result- 
ant of  two  forces  acting  at  an  angle  to  each  other,  it  is  the 
diagonal  of  a  parallelogram  of  which  AB  is  one  of  the  sides. 
From  C  draw  CD  parallel  with  and  equal  to  BA,  and  com- 
plete the  parallelogram  by  connecting  the  points  B  and  C, 
and  A  and  D.  Then,  according  to  the  principle  of  compo- 
sition of  forces,  AD  represents  the  intensity  and  direction 
of  the  force  which,  combined  with  the  force  AB,  would  move 
the  ball  from  A  to  C.  The  component  AB  being  given, 
no  other  single  force  than  AD  will  satisfy  the  question. 

Experiment  62.  —  Verify  the  preceding  propositions  in  the  follow- 
ing manner  :  From  pegs  A  and  B  (Fig.  72),  in  the  frame  of  a  black- 
board, suspend  a  known  weight  W,  of  (say)  10  pounds,  by  means  of 
two  strings  connected  at  C.  In  each  of  these  strings  insert  dyna- 
mometers x  and  y.  Trace  upon  the  blackboard  short  lines  along  the 
strings  from  the  point  C,  to  indicate  the  direction  of  the  two  com- 


74  GENERAL  DYNAMICS. 

ponent  forces ;  also  trace  the  line  CD,  in  continuation  of  the  line  WC, 
to  indicate  the  direction  and  intensity  of  the  resultant.  Remove 

the  dynamometers,  extend  the 
lines  (as  Ca  and  C6),  and  on 
these  construct  a  parallelo- 
gram, from  the  extremities  of 
the  line  CD  regarded  as  a 
diagonal.  It  will  be  found 
that  10 :  number  of  pounds  in- 
dicated by  the  dynamometer 
z::CD:Ca;  also  that  10: 
number  of  pounds  indicated 
by  the  dynamometer  y  : :  CD  : 
C6.  Again,  it  is  plain  that  a 

single  force  of  10  pounds  must  act  in  the  direction  CD  to  produce  the 
same  result  that  is  produced  by  the  two  components.  Hence,  when 
two  sides  of  a  parallelogram  represent  the  intensity  and  direction  of  two 
component  forces,  the  diagonal  represents  the  resultant.  Vary  the  problem 
by  suspending  the  strings  from  different  points,  as  E  and  F,  A  and 
F,  etc. 

An  excellent  verification  of  the  Second  Law  of  Motion 
and  the  principle  of  composition  of  forces  is  found  in  the 
fact  that  a  ball,  projected  horizontally,  will  reach  the 
ground  in  precisely  the  same  time  that  it  would  if  dropped 
from  a  state  of  rest  from  the  same  hight.  That  is,  any 
previous  motion  a  body  has  in  any  direction  does  not 
affect  the  action  of  gravity  upon  the  body. 

Experiment  63.  —  Draw  back  the  rod  d  (Fig.  73)  toward  the  left, 
and  place  the  detent-pin  c  in  one  of  the  slots.  Place  one  of  the  brass 
balls  on  the  projecting  rod,  and  in  contact  with  the  end  of  the  instru- 
ment, as  at  A.  Place  the  other  ball  in  the  short  tube  B.  Raise  the 
apparatus  to  as  great  an  elevation  as  practicable,  and  place  it  in  a 
perfectly  horizontal  position.  Release  the  detent,  and  the  rod,  pro- 
pelled by  the  elastic  force  of  the  spring  within,  will  strike  the  ball  B 
with  great  force,  projecting  it  in  a  horizontal  direction.  At  the  same 
instant  that  B  leaves  the  tube  and  is  free  to  fall,  the  ball  A  is  re- 
leased from  the  rod,  and  begins  to  fall.  The  sounds  made  on  strik- 


COMPOSITION  AND    RESOLUTION   OF  FORCES. 


75 


ing  the  floor  reach  the  ears  of  the  observer  at  the  same  instant; 
this  shows  that  both  balls  reach  the  floor  in  sensibly  the  same  time, 
and  that  the  horizontal  motion  which  one  of  the  balls  has  does  not 
affect  the  time  of  its  fall. 


66.  Composition  of  Parallel  Forces.  —  If  the  strings 
CA  and  CB  (Fig.  72)  are  brought  nearer  to  each  other  (as 
when  suspended  from  B  and  E)  so  that  the  angle  formed 
by  them  is  diminished,  the  component  forces,  as  indicated 
by  the  dynamometers,  will  decrease,  till  the  two  forces 
become  parallel,  when  the  sum  of  the  components  just 
equals  the  weight  W.  Hence,  (1)  two  or  more  forces 
applied  to  a  body  act  to  the  greatest  advantage  when  they 
are  parallel,  and  in  the  same  direction,  in  which  case  their 
resultant  equals  their  sum. 

On  the  other  hand,  if  the  strings  are  separated  from 
each  other,  so  as  to  increase  the  angle  formed  by  them, 
the  forces  necessary  to  support  the  weight  increase  until 
they  become  exactly  opposite  each  other,  when  the  two 
forces  neutralize  each  other,  and  none  is  exerted  in  an 
upward  direction  to  support  the  weight.  If  the  two  strings 


76  GENEEAL  DYNAMICS. 

are  attached  to  opposite  sides  of  the  weight  (the  weight 
being  supported  by  a  third  string),  and  pulled  with  equal 
force,  the  weight  does  not  move.  But  if  one  is  pulled 
with  a  force  of  15  pounds,  and  the  other  with  a  force  of 
10  pounds,  the  weight  moves  in  the  direction  of  the 
greater  force ;  and  if  a  third  dynamometer  is  attached  to 
the  weight,  on  the  side  of  the  weaker  force,  it  is  found 
that  an  additional  force  of  five  pounds  must  be  applied 
to  prevent  motion.  Hence,  (2)  when  two  or  more  forces 
are  applied  to  a  body,  they  act  to  greater  disadvantage  the 
farther  their  directions  are  removed  from  one  another  ;  and 
the  result  of  parallel  forces  acting  in  opposite  directions  is 
a  resultant  force  in  the  direction  of  the  greater  force,  equal 
to  their  difference. 

When  parallel  forces  are  not  applied  at  the  same  point, 
the  question  arises,  What  will  be  the  point  of  application 
of  their  resultant?  To  the  opposite  extremities  of  a  bar 

AB  (Fig.74)  apply  two 
sets  of  weights,  which 
shall  be  to  each  other 
as  3*lbs.:l  Ib.  The 
resultant  is  a  single 
force,  applied  at  some 
Fig*  74>  point  between  A  and 

B.  To  find  this  point  it  is  only  necessary  to  find  a 
point  where  a  single  force,  applied  in  an  opposite  direc- 
tion, will  prevent  motion  resulting  from  the  parallel 
forces;  in  other  words,  to  find  a  point  where  a  support 
may  be  applied  so  that  the  whole  will  be  balanced.  That 
point  is  found  by  trial  to  be  at  the  point  C,  which  divides 
the  bar  into  two  parts  so  that  AC  :  CB  : :  1  Ib. :  3  Ibs. 
Hence,  (3)  when  two  parallel  forces  act  upon  a  body  in 
the  same  direction,  the  distances  of  their  points  of  applica- 


COMPOSITION  AND    RESOLUTION  OF  FORCES.  77 

tion  from  the  point   of  application  of  their  resultant  are 
inversely  as  their  intensities. 

The  dynamometer  E  indicates  that  a  force  equal  to  the 
sum  of  the  two  sets  of  weights  is  necessary  to  balance  the 
two  forces.  A  force  whose  effect  is  to  balance  the  effects 
of  several  components  is  called  an  equilibrant.  The  result- 
ant of  the  two  components  is  a  single  force,  equal  to  their 
sum,  applied  at  C  in  the  direction  CD. 

67.   Moment  of  a  Force.— The    tendency  of  a  force 
to  produce  rotation  about  a  fixed  point  as  C  (Fig.  75) 
is   called    its   moment 
about  that  point.  The 


perpendicular  distance   J  •*»]»* 

(AC  or  BC)  from  the     *  1 

fixed  point  (C)  to  the  Fig.  75. 

line  of  direction  in  which  the  force  acts  (AD  or  BE)  is 
called  the  leverage  or  arm.  The  moment  of  a  force  is  meas- 
ured by  the  product  of  the  number  of  units  of  force  into  the 
number  of  units  of  leverage.  For  example,  the  moment  of 
the  force  applied  at  A  is  expressed  numerically  by  the 
number  (30  x  2  =)  60. 

68.  Equilibrium  of  Moments.  —  The  moment  of  a 
force  is  said  to  be  positive  when  it  tends  to  produce  rota- 
tion in  the  direction  in  which  the  hands  of  a  clock  move, 
and  negative  when  its  tendency  is  in  the  reverse  direction. 
If  two  forces  act  at  different  points  of  a  body  which  is 
free  to  rotate  about  a  fixed  point,  they  will  produce  equi- 
librium when  their  moments  are  opposite  and  their  alge- 
braic sum  is  zero.  Thus  the  moment  of  the  force  applied 
at  A  (Fig.  75)  is  (-30  X  2) -60.  The  moment  of  the 
force  applied  at  B  in  an  opposite  direction  is  accordingly 
(+20  X  3=) +60.  Their  algebraic  sum  is  zero,  conse- 
quently there  is  equilibrium  between  the  forces. 


78  GENERAL  DYNAMICS. 

When  more  than  two  forces  act  in  this  manner,  there 
will  be  equilibrium   if  the   sum  of  all  the  positive   mo- 

fi*  ments  is  equal  to  the 

b\  sum  of  all  the  nega- 

™\ — 15 r — £ f 20 I30     tiye  moments.     Thus 

d\  c\  A       the  sum  of  the  posi- 

ijs  a  2%  h     tive  moments  acting 

Fig'  76'  about  point  F  (Fig. 

76)  is  (/)  45 +  (e)  25  + (a)  30  =100;    the    sum    of    the 

negative  moments  acting  about  the  same  point  is  (c)  30  + 

(d)  40  +  (b)  30  =  100 ;    the    two   sums  being   equal,   the 

forces  are  in  equilibrium. 

69.  Mechanical  Couple. — 
If  two  equal,  parallel,  and  con- 
trary forces  are  applied  to  op- 
posite extremities  of  a  stick 
AB  (Fig.  77),  no  single  force 
can  be  applied  so  as  to  keep 
Flg*  77*  the  stick  from  moving ;  there 

will  be  no  motion  of  translation,  but  simply  a  rotation 
around  its  middle  point  C.  Such  a  pair  of  forces,  equal, 
parallel,  and  opposite,  is  called  a  mechanical  couple. 


Section  V. 

THE  THIRD   LAW   OF  MOTION. 

7O.  Introductory  Experiments.  —  We  have  learned 
that  motion  cannot  originate  in  a  single  body,  but  arises 
from  mutual  action  between  two  bodies  or  two  parts  of  a 
body.  For  example,  a  man  can  lift  himself  by  pulling 


THE  THIRD  LAW  OF  MOTION. 


79 


on  a  rope  attached  to  some  other  .object,  but  not  by  his 
boot-straps,  or  a  rope  attached  to  his  feet.  In  every  change 
in  regard  to  motion  there  are  always  at  least  two  bodies 
oppositely  affected. 

Experiment  64.  —  Suspend  the  deep  glass  bucket  A  (Fig.  78)  by 
means  of  a  strong  thread  two  feet  long,  so  that  the  long  projecting 
pointer  may  be  directly  over  a  dot  made  on  a 
piece  of  paper  placed  beneath  ;  or  place  beneath 
another  pointer,  B,  so  that  the  two  points  shall 
just  meet.  Fill  the  bucket  with  water.   Gravity 
causes  the  water  to  flow  from  the  orifice  C; 
A   but  the  bucket  moves  in  the  opposite  direction. 


Fig.  78. 


Fig.  79. 


Experiment  65.  —  Place  the  hollow  glass  globe  and  stand  (Fig. 
79)  under  the  receiver  of  an  air-pump,  and  exhaust  the  air.  The  air 
within  the  globe  expands,  and  escapes  from  the  small  orifices  a  and  c 
at  the  extremity  of  fhe  two  arms.  But  this  motion  of  the  air  is 
attended  by  an  opposite  motion  of  the  arms  and  globe,  and  a  rapid 
rotation  is  caused. 

A  man  in  a  boat  weighing  one  ton  pulls  at  one  end  of  a 
rope,  the  other  end  of  which  is  held  by  another  man,  who 


80  GENERAL  DYNAMICS. 

weighs  twice  as  much  as  the  first  man,  in  a  boat  weighing 
two  tons :  both  boats  will  move  towards  each  other,  but 
in  opposite  directions ;  if  the  resistances  which  the  two 
boats  encounter  were  the  same,  the  lighter  boat  would 
move  twice  as  fast  as  the  heavier,  but  with  the  same 
momentum. 

If  the  boats  are  near  each  other,  and  the  men  push  each 
other's  boats  with  oars,  the  boats  will  move  in  opposite 
directions,  though  with  different  velocities,  yet  with  equal 
momenta. 

The  opposite  impulses  received  by  the  bodies  concerned 
are  usually  distinguished  by  the  terms  action  and  reaction. 
We  measure  these,  when  both  are  free  to  move,  by  the 
momenta  generated,  which  is  always  the  same  in  both 
bodies. 

71.  Third  Law  of  Motion.  —  To  every  action  there  is 
an  equal  and  opposite  reaction. 

The  application  of  this  law  is  not  always  obvious. 
Thus,  the  apple  falls  to  the  ground  in  consequence  of  the 
mutual  attraction  between  the  apple  and  the  earth.  The 
earth  does  not  appear  to  fall  toward  the  apple.  But, 
as  the  mass  of  the  earth  is  enormously  greater  than  that 
of  the  apple,  its  velocity,  for  an  equal  momentum,  is 
proportionately  less. 

EXERCISES. 

1.  (a)  Why  does  not  a  given  force,  acting  the  same  length  of  time, 
give  a  loaded  car  as  great  a  velocity  as  an  empty  car?    (ft)   After 
equal  forces  have  acted  for  the  same  length  of  time  upon  both 
cars,  and  given  them  unequal  velocities,  which  will  be  the  more 
difficult  to  stop? 

2.  (a)  The  planets  move  unceasingly ;   is  this  evidence  that  there 
are  forces  pushing  or  pulling  them  along?      (7»)    None    of    their 
motions  are  in  straight  lines ;  are  they  acted  upon  by  external  forces  ? 


THE  THIRD  LAW  OF  MOTION. 


81 


3.  A  certain  body  is  in  motion ;  suppose  that  all  hindrances  to 
motion  and  all  external  forces  were  withdrawn  from  it,  how  long 
would  it  move?    Why?    In  what  direction?    Why?    With  what 
kind  of  motion,  i.e.  accelerated,  retarded,  or  uniform?    Why? 

4.  Copy  upon  paper  and  find  the  resultant  of  the  components  AB 
and  AC  in  each  of  the  four  diagrams  in  Figure  80.    Also  assign  ap- 
propriate numerical  values  to  each  component,  and   find  the  corre- 
sponding numerical  value  of  each  resultant. 


Fig.  80. 

5.  Explain  how  rotating  lawn-sprinklers  are  kept  in  motion. 

6.  When  you  leap  from  the  earth,  which  receives  the  greater  mo- 
mentum, your  body  or  the  earth  ? 

7.  When  you  kick  a  door-rock,  why  does  snow  or  mud  on  your 
shoes  fly  off? 

8.  Why  cannot  a  person  propel  a  vessel  during  a  calm  by  blowing 
the  sails  with  a  big  bellows  placed  on  the  deck  of  the  same  vessel  ? 

9.  In  swimming,  you  put  water  in  motion ;  what  causes  your  body 
to  advance?    What  propels  the  bird  in  flying? 

10.  Could  a  rocket  be  projected  in  the  usual  way  if  there  were  no 
atmosphere  ? 


j.  j. 


GENERAL  DYNAMICS. 


Section  VI. 

APPLICATIONS  OP  THE  THKEE  LAWS  OF  MOTION. —  CENTER 
OF   GRAVITY. 

72.  Center  of  Gravity  Defined.  —  Let  Figure  81  repre- 
sent any  body  of  matter;  for  instance,  a  stone.  Every 
molecule  of  the  body  is  acted  upon  by  the  force  of  gravity. 
The  forces  of  gravity  of  all  the  mole- 
cules form  a  set  of  parallel  forces  act- 
ing vertically  downward,  the  resultant 
of  which  equals  their  sum,  and  has  the 
same  direction  as  its  components.  The 
resultant  passes  through  a  definite 
point  in  whatever  position  the  body 
may  be,  and  this  point  is  called  its  cen- 
ter  of  gravity.  The  center  of  gravity 
of  a  body  is,  therefore,  the  point  of  application  of  the 
resultant  of  all  these  forces  ;  and  for  practical  purposes  the 
whole  weight  of  the  body  may  be  supposed  to  be  concentrated 
at  its  center  of  gravity. 

Let  G  in  the  figure  represent  this  point.  For  practical 
purposes,  then,  we  may  consider  that  gravity  acts  only 
upon  this  point,  and  in  the  direction  GF.  If  the  stone 
falls  freely,  this  point  cannot,  in  obedience  to  the  first  law 
of  motion,  deviate  from  a  vertical  path,  however  much  the 
body  may  rotate  about  this  point  during  its  fall.  Inas- 
much, then,  as  the  e.g.  of  a  falling  body  always  describes 
a  definite  path,  a  line  GF  that  represents  this  path,  or  the 
path  in  which  a  body  supported  tends  to  move,  is  called 
the  line  of  direction. 

It  is  evident  that  if  a  force  is  applied  to  a  body  equal  to 


APPLICATIONS   OF  THE  THREE   LAWS  OF  MOTION.     83 

its  own  weight,  and  opposite  in  direction,  and  anywhere  in 
the  line  of  direction  (or  its  continuation),  this  force  will 
be  the  equilibrant  of  the  forces  of  gravity ;  in  other  words, 
the  body  subjected  to  such  a  force  is  in  equilibrium, 
and  is  said  to  be  supported,  and  the  equilibrant  is  called 
its  supporting  force.  To  support  any  body,  then,  it  is 
only  necessary  to  provide  a  support  for  its  center  of  grav- 
ity. The  supporting  force  must  be  applied  somewhere  in 
the  line  of  direction,  otherwise  the  body  will  fall.  The  dif- 
ficulty of  poising  a  book,  or  any  other  object,  on  the 
end  of  a  finger,  consists  in  keeping  the  support  under  the 
center  of  gravity. 

Figure  82  represents  a  toy  called  a  "  witch,"  consisting  of  a  cylinder  of 
pith  terminating  in   a  hemisphere  of   lead. 
The  toy  will  not  lie  in  a  horizontal  position, 
as  shown  in  the  figure,  because  the  support 
is  not  applied  immediately  under  its  e.g.  at 
G ;  but  when  placed  horizontally,  it  immedi- 
ately assumes  a  vertical  position.    It  appears  Flg'  82* 
to  the  observer  to  rise ;   but,  regarded  in  a  mechanical  sense,  it  really 
falls,  because  its  e.g.,  where  all  the  weight  is  supposed  to  be  concentrated, 
takes  a  lower  position. 

73.    How  to  Find  the  Center  of  Gravity  of  a  Body.  — 

Imagine  a  string  to  be  attached  to 
a  potato  by  means  of  a  tack,  as  in 
Figure  83,  and  to  be  suspended 
from  the  hand.  When  the  potato 
is  at  rest,  there  is  an  equilibrium 
of  forces,  and  the  e.g.  must  be  some- 
where in  the  line  of  direction  an ; 
hence,  if  a  knitting-needle  is  thrust 
vertically  through  the  potato  from 
a,  so  as  to  represent  a  continuation  Fls*  83* 

of  the  vertical  line  oa,  the  e.g.  must  lie  somewhere  in  the 


84  GENERAL   DYNAMICS. 

path  an  made  by  the  needle.  Suspend  the  potato  from 
some  other  point,  as  6,  and  a  needle  thrust  vertically 
through  the  potato  from  b  will  also  pass  through  the  e.g. 
Since  the  e.g.  lies  in  both  the  lines  an  and  bs,  it  must  be  at 
<?,  their  point  of  intersection.  It  will  be  found  that,  from 
whatever  point  the  potato  is  supported,  the  point  c  will 
always  be  vertically  under  the  point  of  support.  On  the 
same  principle  the  e.g.  of  any  body  is  found.  But  the  e.g. 
of  a  body  may  not  be  coincident  with  any  particle  of  the 
body ;  for  example,  the  e.g.  of  a  ring,  a  hollow  sphere,  etc. 

74.  Equilibrium  of  Bodies.  —  That  a  body  acted  on 
solely  by  its  weight  may  be  in  equilibrium  (i.e.  supported), 
it  is  sufficient  that  its  line  of  direction  shall  pass  through 
the  point  or  surface  by  which  it  is  supported.  For  ex- 
ample, when  a  body  is  to  be  supported  at  its  base,  the  line 
of  direction  must  pass  through  the  base.  The  base  of  a 
body  is  not  necessarily  limited  to  that  part  of  the  under 
surface  of  a  body  that  touches  its  support.  For  example, 
if  a  string  is  placed  around  the  four  legs  of  a  table  near 
the  floor,  the  rectangular  figure  bounded  by  the  string  is 
the  base  of  the  table. 

It  is  evident  that  the  resultant  weight  of  a  body  acting 
at  its  e.g.  tends  to  bring  this  point  as  low  as  possible ;  hence 
a  body  tends  to  assume  a  position  such  that  its  e.g.  will  be 
as  low  as  possible. 

In  whatever  manner  a  body  is  supported,  the  equilib- 
rium is  stable  if,  on  moving  the  body,  the  center  of  gravity 
ascends;  unstable,  if  it  descends;  and  neutral,  if  it  neither 
ascends  nor  descends,  as  that  of  a  sphere  rolled  on  a 
horizontal  plane. 

Experiment  66.  —  Try  to  support  a  ring  on  the  end  of  a  stick,  as 
at  b  (Fig.  84).  If  you  can  keep  the  support  exactly  under  the  e.g.  of 


APPLICATIONS   OF  THE  THREE  LAWS   OF   MOTION.       85 


the  ring,  there  will  be  an  equilibrium  of  forces,  and  the  ring  will  re- 
main at  rest.  But  if  it  is  slightly  disturbed,  tihe  equilibrium  will  be 
destroyed,  and  the  ring  will  fall.  Support  it  at  a ;  in  this  position  its 
e.g.  is  as  low  as  possible,  and  any  disturbance  will  raise  its  e.g. ;  but, 
in  consequence  of  the  tendency  of  the  e.g.  to  get  as  low  as  possible,  it 
will  quickly  fall  back  into  its  original  position. 


Fig.  85. 

Experiment  67.  —  Prepare  a  V-shaped  frame  like  that  shown  in 
Figure  85,  the  bar  AC  being  about  three  feet  long ;  place  it  so  that 
the  end  will  overlap  the  table  two  or  three  inches,  and  hang  a  heavy 
weight  or  a  pail  of  water  on  the  hook  B,  and  the  whole  will  be  sup- 
ported. Rock  the  weight  back  and  forth  by  raising  the  end  C  and 
allowing  it  to  fall.  What  kind  of  equilibrium  is  this  ?  Remove  the 
weight,  and  the  bar  falls  to  the  floor.  Why  ? 

The  stability  of  a  body  varies  with  its  breadth  of  base,  and 
inversely  with  the  hight  of  its  e.g.  above  its  base.  Support 
a  book  on  a  table  so  that  it  may  have  three  different 
degrees  of  stability,  and  account  for  the  same. 

QUESTIONS. 

1.  Why  is  a  person's  position  more  stable  when  his 
feet  are  separated  a  little,  than  when  close  together  V 

2.  How  does  ballast  tend  to  keep  a  vessel  from  over- 
turning ? 

3.  For  what  two  reasons  is  a  pyramid  a  very  stable 
structure  ? 

4.  What  point  in  a  falling  body  descends  in  a  straight 


86  GENERAL  DYNAMICS. 

line?    What  is  this  line  called?    Disregarding  the  motions  of  the 
earth,  toward  what  point  in  the  earth  does  this  line  tend? 

5.  It  is  difficult  to  balance  a  lead-pencil  on  the  end  of  a  finger ; 
but  by  attaching  two  knives  to  it,  as  in  Figure  86,  it  may  be  rocked 
to  and  fro  without  falling.  Explain. 


Section  VII. 

APPLICATIONS  OF  THE  THREE  LAWS  OF  MOTION  CONTIN- 
UED.—  EFFECT  OF  A  CONSTANT  FORCE  ACTING  ON  A 
BODY  PERFECTLY  FREE  TO  MOVE.  —  FALLING  BODIES. 

75.  Any  Force,  however  Small,  can  move  any  Body 
of  however  Great  Mass.  —  For  example,  a  child  can  move 
a  body  having  a  mass  equal  to  that  of  the  earth,  pro- 
vided only  that  the  motion  of  this  body  is  not  hindered 
by  a  third  body.  Moreover,  the  amount  of  momentum 
that  the  child  can  generate  in  this  immense  body  in  a 
given  time  is  precisely  the  same  as  that  which  it  would 
generate  by  the  exertion  of  the  same  force  for  the  same 
length  of  time  on  a  body  having  a  mass  of  (say)  10  pounds. 
Momentum  is  the  product  of  mass  into  velocity;  so,  of 
course,  as  the  mass  is  large,  the  velocity  acquired  in  a 
given  time  will  be  correspondingly  small.  The  instant  the 
child  begins  to  act,  the  immense  body  begins  to  move. 
Its  velocity,  infinitesimally  small  at  the  beginning,  would 
increase  at  almost  an  infinitesimally  slow  rate,  so  that  it 
might  be  months  or  years  before  its  motion  would  become 
perceptible.  It  is  easy  to  see  how  persons  may  get  the 
impression  that  very  large  bodies  are  immovable  except 
by  very  great  forces.  The  erroneous  idea  is  acquired  that 


APPLICATIONS   OF   THE  THREE   LAWS   OF   MOTION.       87 

bodies  of  matter  have  a  power  to  resist  the  action  of  forces 
in  causing  motion,  and  that  the  greater  the  mass,  the 
greater  the  resistance  ("  quality  of  not  yielding  to  force," 
Webster').  The  fact  is,  that  no  body  of  whatever  mass  has 
any  power  to  resist  motion;  in  other  words,  "-a  body  free  to 
move  cannot  remain  at  rest  under  the  slightest  unbalanced 
force  tending  to  set  it  in  motion"  Furthermore,  a  given 
force  acting  for  the  same  length  of  time  will  generate  the 
same  amount  of  momentum  in  all  bodies  free  to  move,  irre- 
spective of  their  masses. 

76.  Falling  Bodies.  —  A  constant  force  is  one  that  acts 
continuously  and  with  uniform  intensity.  Nature  fur- 
nishes no  example  of  a  body  moved  by  a  force  so  nearly 
constant  as  that  of  a  body  falling  through  a  moderate  dis- 
tance to  the  earth.  Inasmuch  as  the  velocity  of  falling 
bodies  is  so  great  that  there  is  not  time  for  accurate  obser- 
vation during  their  fall,  we  must,  in  investigating  the  laws 
of  falling  bodies,  resort  to  some  method  of  checking  their 
velocity,  without  otherwise  changing  the  character  of  the 
fall. 

Experiment  68.  —  Ascertain,  as  in  Experiment  60,  how  far  the 
weights,  moved  by  a  constant  force  (e.g.  2  grams),  descend  during 
one  swing  of  the  pendulum.  Inasmuch  as  all  swings  of  the  pendulum 
are  made  in  equal  intervals  of  time,  we  may  take  the  time  of  one 
swing  as  our  unit  of  time.  We  will,  for  convenience,  take  for  our 
unit  of  distance  the  distance  the  weights  fall  during  the  first  unit  of 
time,  call  this  unit  a  space,  and  represent  the  unit  graphically  by  the 
line  ab  (Fig.  87). 

Next  ascertain  how  far  the  weights  fall  from  the  starting-point 
during  two  units  of  time  (i.e.  two  swings  of  the  pendulum).  The 
distance  will  be  found  to  be  four  spaces,  or  four  times  the  distance 
that  they  fell  during  the  first  unit  of  time.  This  distance  is  repre- 
sented by  the  line  ac.  But  we  have  learned  that  the  weights  descend 
only  one  space  (a&)  during  the  first  unit  of  time,  hence  they  must 


88 


GENERAL  DYNAMICS. 


descend  three  spaces  during  the  second  unit  of  time.    The  weights, 
under  the  action  of  the  constant  force,  start  from  a  state  of  rest,  and 
move  through  one  space  in  a  unit  of  time.     This  force,  continuing  to 
act,  accomplishes  no  more  nor  less  during  any  subsequent 
unit  of  time.    But  the  weights  move  through  three  spaces 
i  U0f  T—\b     during  the  second  unit  of  time ;  hence  two  of  the  spaces 
must  be  due  to  the  velocity  they  had  acquired  at  the  end 
of  the  first  unit.     In  other  words,  if  the  ring  H  is  placed 
at  the  point  (corresponding  to  b)  reached  by  the  weights 
at  the  end  of  the  first  unit  of  time,  then  weight  E  will  be 
2UofT— \c     cauSn*  °ff  (i'e-  the  constant  force  will  be  withdrawn), 
and  the  other  weights  will,  in  conformity  with  the  first 
law  of  motion,  continue  to  move  with  uniform  velocity 
from  this  point  (except  as  they  are  retarded  by  resist- 
ance of  the  air  and  the  friction  of  the  wheel  C),  and  will 
descend  two  spaces  during  the  second  unit  and  reach 
point  e.     (Try  it.) 

The  weights,  therefore,  have  at  the  end  of  the  first 
unit  of  time   a   velocity  (V)  of  two  spaces.    But  they 
SUofT—ld     started  from  a  state  of  rest:   hence  the  constant  force 
Fig.  87.       causes,  during  the  first  unit  of  time,  an  acceleration  of 
velocity  equal  to  two  spaces. 

Let  the  weights  descend  three  units  of  time,  and  it  will  be  found 
that  the  weights  will  descend  in  this  time  nine  spaces  (ad),  or  five 
spaces  (cd)  during  the  third  unit  of  time.  One  of  these  five  spaces 
is  due  to  the  action  of  the  force  during  the  third  unit  of  time ;  the 
weights  must  then  have  had  at  point  c  (i.e.  at  the  end  of  the  second  unit 
of  time)  a  velocity  of  four  spaces.  But  at  the  end  of  the  first  unit 
of  time  they  had  a  velocity  of  two  spaces ;  then  they  must  have  gained 
during  the  second  unit  of  time  a  velocity  of  two  spaces.  It  seems, 
then,  that  the  effect  of  a  constant  force  applied  to  a  body  is  to  produce 
uniformly  accelerated  motion  when  there  are  no  resistances. 

The  acceleration  due  to  gravity  is  usually  represented  by  g,  and  is 
always  twice  the  distance  Q  g)  traversed  during  the  first  unit  of  time. 
When  a  body  is  acted  upon  by  any  other  constant  force,  the  accelera- 
tion produced  by  the  force  is  usually  represented  by  the  letter  A. 


APPLICATIONS   OF   THE   THREE   LAWS   OF  MOTION.       89 


Arrange  the  results  of  your  observations  in  a  tabulated  form  as 
follows :  — 


No.  of  units  of 
time. 

Total  distance 
passed  over. 
(8) 

Distance  passed 
over   in    each 
unit;   also  av- 
erage velocity. 

Velocity  at  the 
end    of    each 
unit. 
(V) 

Increase  of  ve- 
locity in  each 
unit,   i.e.   ac- 
celeration. 

1 

1Q<7) 

!(*» 

2(i^ 

2(|,) 

2 

4      " 

3      « 

4      " 

2      " 

3 

9      " 

5      " 

6      « 

2      " 

4 

16      " 

7      " 

8      " 

2      " 

etc. 

etc. 

etc. 

etc. 

etc. 

77.   Formulas  for  Uniformly  Accelerated  Motion. — 

If  we  substitute  A  for  #,  and  represent  the  distance 
traversed  during  a  given  unit  of  time  by  s,  and  the  total 
distance  the  body  has  accomplished  from  the  outset  to 
the  end  of  a  given  unit  of  time  (T)  by  S,  we  derive  from 
our  tabulated  results  the  following  formulas  for  solving 
problems  of  uniformly  accelerated  motion:  — 

(1)  V=(£AX2T)=AT. 

(2)  «=JA(2T-1). 

(3)  S  =  *AT2. 

Hence,  (1)  the  velocity  acquired  varies  as  the  time;  (2)  the 
spaces  passed  over  in  successive  equal  intervals  of  time  vary 
as  the  odd  numbers  1,  3,  5,  7,  etc. ;  and  (3)  the  entire  sp-ace 
traversed  varies  as  the  square  of  the  time. 

Strictly  speaking,  a  falling  body  is  not  under  the  influence  of  a  constant 
force,  inasmuch  as  gravity  varies  inversely  as  the  square  of  the  distance 
from  the  center  of  the  earth.  But  for  small  distances  the  variation  may 
be,  for  all  practical  purposes,  disregarded,  as  at  a  hight  of  a  kilometer 
(about  f  of  a  mile)  it  is  only  about  j^j-g  of  the  weight  at  the  surface.  It 
can  be  shown  mathematically  that  the  velocity  that  would  be  acquired  by 
a  body  falling  freely  to  the  earth's  surface  from  an  infinite  distance  would 
be  about  35,000  feet  per  second. 


90  GENERAL  DYNAMICS. 

78.  Velocity  of  a  Falling  Body  Independent  of  its 
Mass  and  Kind  of  Matter.  —  If  we  grasp  a  coin  and  a  bit 
of  paper  between  the  thumb  and  finger,  and  release  both 
at  the  same  instant,  the  coin  will  reach  the  floor  first.  It 
would  seem  as  though  a  heavy  body  falls  faster  than  a 
light  body.  Galileo  was  the  first  to  show  the  falsity  of 
this  assumption.  He  let  drop  from  an  eminence  iron  balls 
of  different  weights :  they  all  reached  the  ground  at  the 
same  instant.  Hence  he  concluded  that  the  velocity  of  a 
falling  body  is  independent  of  its  mass. 

He  also  dropped  balls  of  wax  with  the  iron  balls.     The 
iron  balls  reached  the  ground  first.     Are  some  kinds  of 
matter  affected  more  strongly  by  gravitation  than 
others?    If  a  coin  and  several   bits  of  paper   are 
placed  in  a  long  glass   tube   (Fig.  88),  the  air  ex- 
hausted, and  the  tube  turned  end  for  end,  it  will 
be  found  that  the  coin  and  the  paper  will  fall  with 
equal  velocities.    Hence,  the  earth  attracts  all  matter 
alike.     A  wax  ball  of  the  same  size  as  an  iron  ball 
meets  with  the  same  resistance  from  the  air  that 
the  iron  ball  does ;  but  since  the  mass  of  the  former 
is  less  than  that  of  the  latter,  the  force  acting  on 
the  former  is  less,  and  a   less  force  cannot  over- 
come the  same  resistance  as  quickly,  consequently 
88>     in  the  air  the  wax  ball  falls  a  little  more  slowly. 
We  conclude,  therefore,  that  in  a  vacuum  all  bodies  fall 
with  equal  velocities. 

Experiments  show  that  in  the  latitude  of  the  Northern 
States  the  acceleration,  i.e.  the  value  of  #,  is,  near  sea-level 
and  in  a  vacuum,  32J  feet  (9.8m)  per  second;  that  is,  the 
velocity  gained  by  a  falling  body,  disregarding  the  resist- 
ance of  the  air,  is  32|-  feet  per  second,  and  the  body  falls 
in  the  first  second  16^  feet  (4.9m). 


APPLICATIONS   OF   THE  THREE  LAWS   OF   MOTION.       91 


M 


Fig.  89. 

(eT)  What  is  its  average  velocity 


EXERCISES. 

1.  What  is  a  constant  force?   What  effect  does  it  produce  on  every 
body  wnen  there  are  no  resistances? 

2.  (a)  How   far  will 
a  body  fall  in  a  vacuum 
in  one  second?  (6) What 
is  its  velocity  at  the  end 
of  the  first  second?   (c) 
What  is  its  acceleration 
per  second  ? 

3.  (a)  How  far  will  a 
body  fall  in  ten  seconds? 
(&)  How  far  will  it  fall 
in    the   tenth   second? 
(c)  What  is  its  velocity 

at  the  end  of  the  tenth  second? 
during  the  tenth  second  ? 

4.  (a)  How  far  will  a  body  fall  in  one-fourth  of  a  second  ? 
is  the  velocity  of  a  falling  body  at  the 

end  of  the  first  quarter  of  a  second  of 
its  fall? 

5.  A  body  is  projected  from  point 
A  (Fig.  89)  in  the  horizontal  direction 
All.     (a)  If  there  were  no  resistance 
of  the  air,  and  gravity  did  not  act  on 
it,  it  would  go  a  distance  during  the 
first  unit  of  time  represented  by  AB ; 
how  far  would  it  go  during  the  second 
and   third  units   of  time?     (In  every 
answer    quote    the    law  of  motion  in 
conformity  with  which  your  answer  is 
given.)     (&)  If  the  body  were  dropped 
from  A,  it  would  reach  successively 
points  E,  F,  and  G  at  the  ends  of  the 
first,  second,  and  third  units  of  time. 
If  the  body  were  projected  horizontally 
in  the  direction  AH,  and  gravity  acts 

during  its  flight,  what  points  will  the  Fig.  9O. 

body  successively  reach  at  the  end  of  the  same  units  of  time  ? 


\ 


92  GENERAL  DYNAMICS. 

6.  (a)  Suppose  that  a  body  is  projected  obliquely  upward  in  the 
direction  AH  (Fig.  90),  (gravity  meantime  acting  on  the  body)  ;  what 
points  will  the  body  reach  successively  at  the  end  of  the  first,  second, 
and  third  units  of  time?     (5)  How  far  will  the  ascending  body  vir- 
tually fall  during  the  first  unit  of  time?     (c)  How  far  during  the 
second  unit  ?   (e?)  How  far  during  the  third  unit  ?    (e)  Show  that  your 
answers  are  consistent  with  the  Second  Law  of  Motion. 

7.  (a)  Under  the  action  of  a  constant  force,  a  body  meeting  with  no 
resistances  moves  from  a  state  of  rest  20  feet  during  the  first  minute  : 
how  far  will  it  go  in  an  hour?    (&)  Suppose  at  the  end  of  the  first 
minute  the  force  should  cease  to  act,  how  far  would  the  body  go  in  an 
hour  from  that  instant  ? 


Section  VIII. 

APPLICATIONS   OF  THE  THREE  LAWS   OF   MOTION   CONTIN- 
UED. —  CURVILINEAR    MOTION. 

79.  How  Curvilinear  Motion  is  Produced.  —  Motion 
is  curvilinear  when  its  direction  changes  at  every  point. 
But  according  to  the  first  law  of  motion,  every  moving 
body  proceeds  in   a   straight   line,   unless   compelled   to 
depart  from  it  by  some  external  force.     Hence  curvilinear 
motion  can  be  produced  only  by  an  external  force  acting 
continuously  upon  the  body  at  an  angle  to  the  straight 
path  in  which  the  body  tends  to  move,  so  as  constantly 
to  change  its   direction.      In  case   the   body  moves  in  a 
circle,  this  force  acts  at  right  angles  to  the  path  of  the 
body  or  towards  the  center  of  motion  ;  hence  this  deflecting 
force  has  received  the  name  of  centripetal  force. 

80.  Centrifugal  Force. 

Experiment  69.  —  Cause  a  ball  to  rotate  around  your  hand  by 
means  of  a  string  attached  to  it  and  held  in  the  hand.     Observe 


APPLICATIONS   OF   THE   THREE   LAWS   OF   MOTION.        93 

closely  every  phase  of  the  operation.  First,  you  make  a  movement  as 
if  to  project  the  ball  in  a  straight  line.  Immediately  you  begin  to 
pull  on  the  string  to  prevent  its  going  in  a  straight  line.  By  a  con- 
tinuous exertion  of  these  two  forces  in  a  short  time  the  ball  acquires 
great  speed.  You  may  now  cease  to  exert  any  projecting  force,  and 
simply  keep  the  hand  still ;  but  as  the  ball  has  acquired  a  motion,  and 
all  motion  tends  to  be  in  a  straight  line,  you  are  still  obliged  to  exert  a 
pulling  force  to  deflect  it  from  this  path.  Observe  that  as  the  velocity 
of  the  ball  is  retarded  by  the  resistance  of  the  air,  the  pulling  or 
deflecting  force  which  you  are  obliged  to  employ  rapidly  diminishes. 

To  satisfy  yourself  that  the  ball  tends  to  move  in  a  straight  line,  let 
go  the  string  or  cut  it,  and  the  ball  immediately  moves  off  in  a  straight 
line,  or  simply  perseveres  in  the  direction  it  had  at  the  instant  the 
string  was  cut.  Observe  that  the  ball  appears  while  rotating  to  be 
pulling  your  hand;  but  you  know  that  all  the  force  concerned  originates 
in  yourself,  and  that  this  apparent  pull  on  the  part  of  the  ball  is  only 
the  effect  of  the  reaction  of  the  force  which  you  exert  on  the  ball. 
This  apparent  reactionary  force  is  called  centrifugal  force. 

Centrifugal  force  is  the  reaction  of  a  revolving  body  on 
the  body  that  guides  it,  and  is  equal  and  opposite  to  the  cen- 
tripetal force  (see  Third  Law  of  Motion). 

When  you  swing  the  ball  about  your  hand  you  discover 
that  the  force  of  the  pull  increases  with  the  velocity,  and 
more  rapidly  than  the  velocity.  Careful  observations  have 
determined  that  for  bodies  revolving  in  circular  orbits  the 
centripetal  (and,  of  course,  centrifugal)  force  varies  as  the 
mass  of  the  body  and  the  square  of  its  velocity. 

The  farther  a  point  is  from  the  axis1  of  motion  of  a  rigid  body,  the 
farther  it  has  to  move  during  a  rotation;  consequently  the  greater  its 
velocity.  Hence,  bodies  situated  at  the  earth's  equator  have  the  greatest 
velocity,  due  to  the  earth's  rotation,  and  consequently  the  greatest  tendency 
to  fly  off  from  the  surface,  the  effect  of  which  is  to  neutralize,  in  some 
measure,  the  force  of  gravity.  It  is  calculated  that  a  body  weighs  about 
2-|-¥  less  at  the  equator  than  at  either  pole,  in  consequence  of  the  greater 
centrifugal  force  at  the  former  place.  But  289  is  the  square  of  17 ;  hence, 

1Axis :  an  imaginary  straight  line  passing  through  a  body  about  which  it  rotates. 


94 


GENERAL   DYNAMICS. 


if  the  earth's  velocity  were  increased  seventeen-fold,  objects  at  the  equator 

would  weigh  nothing. 

We  have  also  learned  (page  17)  that  a  body  weighs  more  at  the  poles, 

in  consequence  of  the  oblateness  of  the  earth.     This  is  estimated  to  make 

a  difference  of  about  F£T.     Hence  a  body  will  weigh  at  the  equator  ?£¥  + 

-2j-g  =  (about)  T|^  less  than  at  the  poles. 

•  The  attraction  between  the  sun  and  the  earth  causes  these  bodies  to 

move  in  curvilinear  paths, 
performing  what  is  called 
annual  revolutions.  The 
motion  of  both  these  bodies, 
were  it  not  for  this  mutual 
attraction  (and  the  attraction 


Fig.  91. 


of    other    celestial    bodies), 


would  be  eternally  in  straight  lines,  but  in  consequence  of  their  mutual 
attraction  both  rotate  about  a  point  C  (Fig.  91),  which  is  the  center  of 
gravity  of  the  two  bodies  considered  as  one  body  (as  if  connected  by  a 
rigid  rod).  If  both  bodies  had  equal  masses,  the  center  of  gravity  and 
center  of  motion  would  be  half-way  between  the  two  bodies ;  but  as  the 
mass  of  the  earth  is  less  than  that  of  the  sun,  so  its  velocity  and  distance 
traversed  are  proportionally  greater. 


Fig.  93.  'Fig.  93. 

Experiment  70.  —  Arrange  some  kind  of  rotating  apparatus,  e.g. 
R  (Fig.  92).  Suspend  a  skein  of  thread  a  (Fig.  93)  by  a  string,  and 
rotate;  it  assumes  the  shape  of  the  oblate  spheroid  a'.  Suspend  a 
glass  globe  G  (Fig.  92)  about  one-tenth  full  of  colored  water,  and 
rotate.  The  liquid  gradually  leaves  the  bottom,  rises,  and  forms  an 
equatorial  ring  within  the  glass.  This  illustrates  the  probable  method 
oy  which  the  earth,  on  the  supposition  that  it  was  once  in  a  fluid 


APPLICATIONS   OF  THE  THREE  LAWS   OF   MOTION.       95 

state,  assumed  its  present  spheroidal  state.  (Explain.)  Pass  a  string 
through  the  longest  diameter  of  an  onion  c,  and  rotate;  the  onion 
gradually  changes  its  position  so  as  to  rotate  on  its  shortest  axis. 

It  may  be  demonstrated  mathematically,  as  well  as  experi- 
mentally, that  a  freely  rotating  body  is  in  stable  equilib- 
rium only  when  rotating  about  its  shortest  diameter ;  hence 
the  tendency  of  a  rotating  body  to  take  this  position. 

QUESTIONS. 

1.  (a)  What  is  the  cause  of  the  stretching  force  exerted  on  the 
rubber   cord    when    you    swing    a    return-ball    about    your   hand? 
(6)  Suppose  that  you  double  the  velocity  of  the  ball ;  how  many  times 
will  you  increase  this  stretching  force  ? 

2.  Why  do  wheels  and  grindstones,  when  rapidly  rotating,  tend  to 
break,  and  the  pieces  fly  off? 

3.  On  what  does  the  magnitude  of  the  pull  between  a  rotating  body 
and  its  center  of  motion  depend? 

4.  (a)  Explain  the  danger  of  a  carriage  being  overturned  in  turning 
a  corner.     (&)  How  many  fold  is  the  tendency  to  overturn  increased 
by  doubling  the  velocity  of  the  carriage  ? 


Section  IX. 

APPLICATION   OF  THE  THREE  LAWS   OF  MOTION  CONTIN- 
UED. —  THE  PENDULUM. 

81.    Laws  of  the  Pendulum. 

Experiment  71.  —  Suspend  iron  balls  by  strings,  as  in  Figure  94. 
Make  A  and  B  the  same  length.  Draw  A  and  B  one  side,  and  to  dif- 
ferent hights,  so  that  one  may  swing  through  a  longer  arc  than  the 
other,  and  let  both  drop  at  the  same  instant.  One  moves  much 
faster  than  the  other,  and  completes  a  longer  journey  at  each  swing, 
but  both  complete  their  swing  or  vibration  at  the  same  time. 

Hence  (1)  the  time  of  vibration  of  a  pendulum  is  (strictly  speaking, 
approximately)  independent  of  the  length  of  the  arc. 


96 


GENERAL   DYNAMICS. 


Experiment  72.  —  Set  all  the  balls  swinging ;  only  A  and  B  swing 
together,  i.e.  in  the  same  time.  The  shorter  the  pendulum,  the  faster 
it  swings.  Make  B  about  39  inches  long  from  the  point  of  sus- 
pension to  the  center  of  the  ball,  regulating 
this  length,  as  necessity  may  require,  so  that 
the  number  of  vibrations  made  by  the  pen- 
dulum in  one  minute  shall  be  exactly  60 ;  in 
other  words,  so  that  it  shall  "  beat  seconds." 
(Accurately,  a  pendulum  that  beats  seconds 
is  39.09  inches  long.)  Make  C  one-fourth 
as  long  as  B.  Count  the  vibrations  made 
by  C  in  one  minute ;  it  makes  120  vibrations 
in  the  same  time  that  B  makes  60  vibrations. 
Make  D  one-ninth  the  length  of  B ;  the 
former  makes  three  vibrations  while  the 
latter  makes  one.  Consequently  the  time  of 
vibration  of  the  former  is  one-third  that  of 
the  latter. 

Hence  (2)  the  time  of  vibration  of  a  pendu- 
lum varies  as  the  square  root  of  its  length. 

By  experiments  too  difficult  for  ordinary 
school  work,  it  has  been  ascertained  that 
(3)  the  time  of  vibration  of  a  pendulum  varies 
inversely  as  the  square  root  of  the  force  of 
gravity  (upon  which  the  value  of  g  depends). 
Hence  it  is  apparent  that  by  determining 
the  time  of  vibration  of  a  pendulum  of  the 
same  length,  at  different  distances  from  the 
center  of  gravity  of  the  earth  (e.g.  at  the  top  and  bottom  of  a 
mountain,  or  at  sea-level  at  different  latitudes),  the  relative  value 
of  g  at  these  places  may  be  ascertained. 

Experiment  73.  —  Loosen  the  binding-screw  in  the  bob  of  the  pen- 
dulum of  the  Atwood  machine  (Fig.  66),  and  place  the  bob  at  differ- 
ent elevations  on  the  pendulum-rod.  Count  the  number  of  vibrations 
made  by  the  pendulum  in  a  minute,  when  the  bob  is  placed  at  these 
different  elevations.  The  greater  the  elevation  of  the  bob,  —  in  other 
words,  the  shorter  the  pendulum,  — the  greater  the  number  of  vibra- 
tions made.  We  learn  by  this  experiment  that  the  time  of  vibration 
of  a  pendulum  may  be  regulated  by  raising  or  lowering  its  bob. 


Fig.  94. 


APPLICATIONS   OF  THE   THREE  LAWS   OF  MOTION.       97 

EXERCISES. 

1.  One  pendulum  is  20  inches  long,  and  vibrates  four  times  as  fast 
as  another.     How  long  is  the  other  ? 

2.  (a)  What  effect  on  the  rate  of  vibration  has  the  weight  of  its 
bob  ?     (b)  What  effect  has  the  length  of  the  arc  ?     (c)  What  affects 
the  rate  of  vibration  of  a  pendulum  ? 

3.  How  can  you  quicken  the  vibration  of  a  pendulum  threefold  ? 

4.  A  clock  loses  time,  (a)    What  change  in  the  pendulum  ought  to 
be  made?     (&)  How  would  you  make  the  correction? 

5.  Two  pendulums  are  four  and  nine  feet  long  respectively.     While 
the  short   one  makes  one  vibration,  how  many  will   the  long   one 
make? 

6.  How  long  is  a  pendulum  that  makes  two  vibrations  in  a  second? 

7.  What  is  the  time  of  vibration  of  a  pendulum  (39.09  -r-  4  =r)  9.75  in. 
long? 

8.  The  number  of  vibrations  made  by  a  given  pendulum  in  a  given 
time  varies  as  the  square  root  of  the  force  of  gravity.     Force  of  grav- 
ity at  any  place  is  expressed  by  the  value  of  g  (i.e.  by  the  acceleration 
which  it  produces),     (a)  If  at  a  certain  place  a  pendulum  39.09  in. 
long  make  3600  vibrations  in  an  hour,  and  the  value  of  g  is  32.16  ft., 
what  is  the  acceleration  at  a  place  where  the  same  pendulum  makes 
3690  vibrations  in  the  same  time?     (b)  Which  of  the  two  places  is 
nearer  the  center  of  gravity  of  the  earth  ? 

9.  Suggest  some  way  by  which  the  force  of  gravity  at  different 
latitudes  and  altitudes  may  be  determined. 

10.  (a)  A  certain  body  weighs  12  Ibs.  where  the  value  of  g  is  32.16  ft. ; 
what  will  the  same  body  weigh  at  a  place  where  g  —  32  ft.  ?     (&)  Sup- 
pose that  the  former  place  is  at  the  surface  of  the  earth  and  4000  miles 
from  the  earth's  center  of  gravity;  how  far  above  it  is  the  latter  place? 
(See  page  16.) 

11.  A  pebble  is  suspended  by  a  thread  2  ft.  long;   required  the 
number  of  vibrations  it  will  make  in  a  minute. 

12.  Why  do  not  heavy  bodies  fall  faster  than  light  ones  in  a  vacuum? 

13.  Take  equal  masses  of  wood  and  lead ;  which  weighs  more  ? 

14.  A  stone  falls  from  the  top  of  a  railway  carriage  which  is  mov- 
ing at  the  rate  of  one-half  of  a  mile  a  minute.     Find  what  horizontal 
distance  and  what  vertical  distance  the  stone  will  have  passed  through 
in  one-tenth  of  a  second,  disregarding  the  resistance  of  the  air. 

Ans.  4.4  ft. ;  .16  ft. 


CHAPTER   IV. 
WORK  AND  ENERGY. 

Section  I. 

METHODS   OF  ESTIMATING   WORK  AND   ENERGY. 

82.  Work. —  Whenever  a  force  causes  motion,  it  does 
work.  A  force  may  act  for  an  indefinite  time  without 
doing  work ;  for  example,  a  person  may  support  a  stone 
for  a  time  and  become  weary  frop  the  continuous  appli- 
cation of  force  to  prevent  its  falling,  but  he  does  no  work 
upon  the  stone  because  he  effects  no  change.  When  a 
force  acts  through  space,  work  is  done.  Let  the  person 
holding  the  weight  exert  just  a  little  more  force ;  the 
weight  will  rise,  and  work  will  be  done. 

A  body  that  is  moved  is  said  to  have  work  done  upon  it ; 
and  a  body  that  moves  another  body  is  said  to  do  work 
upon  the  latter.  When  the  heavy  weight  of  a  pile-driver 
is  raised,  work  is  done  upon  it;  when  it  descends  and 
drives  the  pile  into  the  earth,  work  is  done  upon  the  pile, 
and  the  pile  in  turn  does  work  upon  the  matter  in  its 
path. 

The  act  of  doing  work  may  consist  in  a  mere  transfer  of 
energy  from  the  body  doing  work  to  the  body  on  which  work 
is  done,  or  it  may  consist  in  a  transformation  of  energy  from 
one  kind  to  some  other  kind,  as  when  the  pile-driver  strikes 


METHODS   OF   ESTIMATING   WORK  AND   ENERGY.        99 

the  pile  and  the  pile  is  forced  into  the  earth,  a  part  of  the 
energy  concerned  in  each  case  is  transformed  into  heat, 
which  we  shall  learn  farther  on  is  molecular  energy. 

In  future  chapters  we  shall  discuss  the  subject  of  transformations  of 
energy ;  for  the  present  our  discussions  relate  chiefly  to  transferences  of 
energy. 

83.  Formulas  for  Estimating  Work.  —  Force  and  space 
(or  distance)  are  the  essential  elements  of  work,  and  neces- 
sarily are  the  quantities  employed  in  estimating  work.  A 
given  force  acting  through  a  space  of  one  foot,  in  raising 
a  weight,  does  a  certain  amount  of  work;  it  is  evident 
that  the  same  force  acting  through  a  space  of  two  feet 
would  do  twice  as  much  work.  Hence  the  general  formula 

FS  -  W,  (1) 

in  which  F  represents  the  force  employed,  S  the  space 
through  which  the  force  acts,  and  W  the  work  done. 

In  case  a  force  encounters  resistance,  the  magnitude  of 
the  force  necessary  to  produce  motion  varies  as  the  resist- 
ance. Often  the  work  done  upon  a  body  is  more  con- 
veniently determined  by  multiplying  the  resistance  by  the 
space  through  which  it  is  overcome,  and  our  formula  becomes 
by  substitution  of  R  (resistance)  for  F  (the  force  which 
overcomes  it) 

RS  =  W.  (2) 

For  example,  a  ball  is  shot  vertically  upward  from  a  rifle 
in  a  vacuum ;  the  work  done  upon  the  ball  (by  the  explo- 
sive force  of  the  gunpowder)  may  be  estimated  by  multi- 
plying the  average  force  (difficult  to  ascertain)  exerted 
upon  it,  by  the  space  through  which  the  force  acts  (a  little 
greater  than  the  length  of  the  barrel);  or  by  multiplying 
the  resistance  to  motion  offered  by  gravity,  i.e.  its  weight 
(easily  ascertained)  by  the  distance  the  ball  ascends. 


100  WORK  AND   ENERGY. 

84.  Energy,  Kinetic  and  Potential.  —  Every  moving 
body  can  impart  motion ;  hence  it  can  do  work  upon  an- 
other body,  and  is  therefore  said  to  possess  energy.  The 
energy  of  a  body  is  its  "  capacity  to  do  work"  The  energy 
which  a  body  possesses  in  consequence  of  its  motion  is 
called  kinetic  energy. 

A  stone  lying  on  the  ground  is  devoid  of  energy.  Raise 
it  and  place  it  on  a  shelf;  in  so  doing  you  perform  work 
upon  it.  As  you  look  at  it  lying  motionless  upon  the  shelf, 
it  appears  as  devoid  of  energy  as  when  lying  on  the  earth. 
Attach  one  end  of  a  cord  to  it  and  pass  it  over  a  pulley 
and  wind  a  portion  of  the  cord  around  the  shaft  connected 
with  a  sewing-machine,  coffee-mill,  lathe,  or  other  con- 
venient machine.  Suddenly  withdraw  the  shelf  from  be- 
neath the  stone.  The  stone  moves;  it  communicates  motion 
to  the  machinery,  and  you  may  sew,  grind  coffee,  turn 
wood,  etc.,  with  the  energy  given  to  the  machine  by  the 
stone. 

The  work  done  on  the  stone  in  raising  it  was  not  lost ; 
the  stone  pays  it  back  while  descending.  There  is  a  very 
important  difference  between  the  stone  lying  on  the  floor, 
and  the  stone  lying  on  the  shelf:  the  former  is  powerless 
to  do  work;  the  latter  can  do  work.  Both  are  alike 
motionless,  and  you  can  see  no  difference,  except  an 
advantage  that  the  latter  has  over  the  former  in  having 
a  position  such  that  it  can  move.  What  gave  it  this 
advantage?  Work.  A  body,  then,  may  possess  energy 
due  merely  to  ADVANTAGE  OF  POSITION,  derived  always 
from  work  bestowed  upon  it.  Energy  due  to  advantage  of 
position  is  called  potential  energy.  We  see,  then,  that 
energy  may  exist  in  either  of  two  widely  different  states. 
It  may  exist  as  actual  motion,  or  it  may  exist  in  a  stored-up 
condition,  as  in  the  stone  lying  on  the  shelf. 


METHODS   OF  ESTIMATING   WORK  AND  ENERGY.     101 

Possibly  some  will  object  that  the  work  done  is  performed  by  gravity, 
and  not  by  the  stone ;  that  if  this  force  should  cease  to  exist,  the  stone 
would  not  move  when  the  shelf  is  removed,  and  consequently  no  work 
would  be  done.  All  this  is  very  true,  and  it  is  likewise  true  that  when 
the  stone  is  on  the  ground,  the  same  force  of  gravity  is  acting,  but  can  do 
no  work  simply  because  the  position  of  things  is  such  that  the  stone  cannot 
move.  The  energy  which  the  stone  on  the  shelf  possesses  is  due  to  the  fact 
that  its  position  is  such  that  it  can  move,  and  that  there  is  a  stress  between 
it  and  the  earth  which  will  cause  it  to  move.  Both  advantage  of  position 
and  stress  are  necessary,  but  the  former  is  attained  only  by  work  per- 
formed. The  force  of  gravity  is  employed  to  do  work,  as  when  mills  are 
driven  by  falling  water ;  but  the  water  must  first  be  raised  from  the  ocean- 
bed  to  the  hillside  by  the  work  of  the  sun's  heat.  The  elastic  force  of 
springs  is  employed  as  a  motive  power ;  but  this  power  is  due  to  an  advan- 
tage of  position  which  the  molecules  of  the  springs  have  first  acquired  by 
work  done  upon  them. 

We  are  as  much  accustomed  to  store  up  energy  for  future  use  as  pro- 
visions for  the  winter's  consumption.  We  store  it  when  we  wind  up  the 
spring  or  weight  of  a  clock,  to  be  doled  out  gradually  in  the  movements 
of  the  machinery.  We  store  it  when  we  bend  the  bow,  raise  the  hammer, 
condense  air,  and  raise  any  body  above  the  earth's  surface. 

A  body  possesses  potential  energy  when,  in  virtue  of  work 
done  upon  it,  it  occupies  a  position  of  advantage,  or  its  mole- 
cules occupy  positions  of  advantage,  so  that  the  energy  ex- 
pended can  be  at  any  time  recovered  by  the  return  of  the  body 
to  its  original  position,  or  by  the  return  of  its  molecules  to 
their  original  positions. 

85.  Unit  of  Work  and  Energy.  —  Inasmuch  as  a 
body's  capacity  to  do  work  is  dependent  wholly  upon 
the  work  which  has  been  done  upon  it,  it  is  evident  that 
both  work  and  energy  may  be  measured  by  the  same  unit. 
The  unit  adopted  is  the  work  done  or  energy  imparted  in 
raising  one  pound  through  a  vertical  hight  of  one  foot.  It 
is  called  a  foot-pound.  (The  French  unit  is  the  work  done 
or  energy  imparted  in  raising  lk  to  a  vertical  hight  of 


102  WORK  AND  ENERGY. 

lm,  and  is  called  a  kilogrammeter.)  Since  the  work  done 
in  raising  1  pound  1  foot  high  is  1  foot-pound,  the  work  of 
raising  it  10  feet  high  is  10  foot-pounds,  which  is  the  same 
as  the  work  done  in  raising  10  pounds  1  foot  high ;  and 
the  same,  again,  as  raising  2  pounds  5  feet  high. 

In  this  unit,  and  by  means  of  formulas  (1)  and  (2),  page 
99,  we  are  able  to  estimate  any  species  of  work,  and  thereby 
compare  work  of  any  kind  with  that  of  any  other  kind. 
For  instance,  let  us  compare  the  work  done  by  a  man  in 
sawing  through  a  stick  of  wood,  whose  saw  must  move  100 
feet  (S)  against  an  average  resistance  (R)  of  20  pounds, 
with  that  done  by  a  bullet  in  penetrating  a  plank  to  the 
depth  of  2  inches  (^  foot)  against  an  average  resistance  of 
500  pounds.  Moving  a  saw  100  feet  against  a  resistance 
of  20  pounds  is  equivalent  to  raising  20  pounds  100  feet 
high,  or  doing  (RS  =  20  X  100  =)  2,000  foot-pounds  of  work 
(W)  ;  a  bullet  moving  |  foot  against  500  pounds'  resistance 
does  the  same  amount  of  work  as  is  required  to  raise  500 
pounds  £  foot  high,  or  (500  X  -J-  =)  83.3  +  foot-pounds  of 
work.  Hence  (2,000  -*-  83.3  =)  about  24  times  as  much 
work  is  done  by  the  sawyer  as  by  the  bullet. 

Let  us  estimate  the  energy  stored  in  a  bow,  by  an  archer  whose  hand 
in  pulling  on  the  string,  while  bending  the  bow  moves  6  inches  Q  foot) 
against  an  average  resistance  of  20  pounds.  Here  RS  =  20  X  \ \  =  10 
foot-pounds  of  work  done  upon  the  bow,  or  10  foot-pounds  of  energy 
stored  in  the  bow. 

86.  Distinction  between  Force  and  Energy.  —  Force 
may  be  measured  by  an  instrument  called  a  dynamometer. 
Energy  which  is  the  product  of  force  into  space  cannot 
be  measured  directly  by  any  instrument.  Force  can  be  in- 
creased indefinitely  by  means  of  machines,  as  a  lever, 
hydrostatic  press,  etc. ;  energy  cannot  be  increased  by  any 
instrument  or  means  whatsoever. 


METHODS   OP  ESTIMATING   WORK   AND   ENERGY.      103 

87.    Formula  for  Calculating  Kinetic  Energy.  —  The 

kinetic  energy  of  a  moving  body  is  calculated  by  means  of 
the  following  formula  :  - 

WV2 

—  -energy, 

in  which  W  represents  the  weight  of  the  body,  V  its  ve- 
locity, and  g  the  acceleration  (in  this  latitude  32£  feet,  or 
9.8m  per  second)  due  to  gravity.  [For  the  derivation  of  this 
formula,  see  the  Author's  Elements  of  Physics,  pages  1£3 
and  124.]  For  example,  the  energy  of  a  cannon-ball  weighing 
50  pounds  and  moving  with  a  velocity  of  1,000  feet  per  sec- 


ond =          =  =  (about)  779,301  foot-pounds. 

Ag          ZX  6Z-Q 

Certain  deductions  from  this  formula  should  be  strongly 
impressed  upon  the  mind  ;  viz.,  (1)  with  the  same  velocity 
the  kinetic  energy  of  a  body  varies  as  its  weight  ;  (2)  with 
the  same  weight  its  kinetic  energy  varies  as  the  square  of  its 
velocity.  Doubling  the  velocity  multiplies  the  energy  four- 
fold ;  trebling  the  velocity  multiplies  it  ninefold.  A  bullet 
moving  with  a  velocity  of  600  feet  per  second  will  pene- 
trate, not  twice,  but  four  times,  as  far  into  a  plank  as  one 
having  a  velocity  of  300  feet  per  second. 

A  railway  train  having  -a  velocity  of  20  miles  an  hour 
will,  if  the  steam  is  shut  off,  continue  to  run  four  times  as 
far  as  it  would  if  its  velocity  were  10  miles  an  hour.  The 
reason  is  apparent  why  light  substances,  even  so  light  as 
air,  exhibit  great  energy  when  their  velocity  is  great. 

88.  Wasted  Work.  —  As  a  stone  is  raised  higher  and 
higher,  the  work  accumulates  in  the  form  of  potential  en- 
ergy. As  a  body  free  to  move  (i.e.  meeting  with  no  re- 
sistance) acquires,  under  the  influence  of  a  constant  force, 
uniformly  accelerated  motion,  so  does  work,  in  the  form 


104  WORK  AND   ENERGY. 

of  kinetic  energy,  accumulate.  But  accumulated  work  or 
energy  does  not  always  vary  as  the  work  performed.  In 
practice,  more  or  less  of  the  work  done,  especially  that 
done  in  overcoming  friction,  resistance  of  fluids,  etc.,  is 
wasted.  The  work  done  by  the  sawyer  and  bullet,  page 
102,  so  far  as  imparting  energy  to  the  bodies  on  which  they 
do  work,  is  all  lost.  Of  the  vast  amount  of  work  done  in 
propelling  a  steamer  across  the  ocean  none  accumulates ; 
all  is  wasted,  distributed  along  the  watery  path,  and  can- 
not be  recovered  or  made  available  for  doing  more  work. 
Evidently  the  accumulated  work  or  available  energy  that  a 
body  possesses  is  the  work  done  upon  the  body  less  the 
wasted  work.  We  may  then  calculate  in  foot-pounds  (or 
kilogrammeters)  according  to  formulas  (1)  or  (2),  page  99, 
the  work  performed  on  a  body,  and  from  this  deduct  the 
number  of  foot-pounds  wasted ;  the  remainder  is  the  num- 
ber of  foot-pounds  of  available  energy  that  is  imparted 
to  the  body. 

89.  Power  of  an  Agent  to  do  Work,  or  Rate  at 
which  an  Agent  can  do  Work. — In  estimating  the  total 
amount  of  work  done,  the  time  consumed  is  not  taken 
into  consideration.  The  work  done  by  a  hod-carrier,  in 
carrying  1,000  bricks  to  the  top  of  a  building,  is  the  same 
whether  he  does  it  in  a  day  or  a  week.  But  in  estimating 
the  power  of  any  agent  to  do  work,  as  of  a  man,  a  horse, 
or  a  steam-engine,  in  other  words,  the  rate  at  which  it  is 
capable  of  doing  work,  it  is  evident  that  time  is  an  impor- 
tant element.  The  work  done  by  a  horse,  in  raising  a 
barrel  of  flour  20  feet  high,  is  about  4,000  foot-pounds ; 
but  even  a  mouse  could  do  the  same  amount  of  work  in 
time. 

The  unit  in  which  power  or  rate  of  doing  work  is  esti- 


METHODS   OF  ESTIMATING  WORK  AND   ENERGY.     105 

mated  is  called  (inappropriately)  a  horse-power.  A  horse- 
power represents  the  power  to  perform  33,000  foot-pounds  of 
work  in  a  minute  (or  550  foot-pounds  in  a  second). 

EXERCISES. 

1.  Can  a  person  lift  himself,  or  put  himself  in  motion,  without 
exerting  force  upon  some  other  body  ? 

2.  Can  a  body  do  work  upon  itself?    Can  a  body  generate  energy 
in  itself,  i.e.  increase  its  own  energy  ? 

3.  (a)  Suppose  that  an  average  force  of  25  pounds  is  exerted 
through  a  space  of  10  inches  in  bending  a  bow;  what  amount  of 
energy  will  it  give  the  bow  ?    (6)  What  kind  of  energy  will  the  bow, 
when  bended,  possess  ? 

4.  (a)  What  amount  of  kinetic  energy  does  a  body  weighing  20 
pounds,  and  moving  with  a  velocity  of  300  feet  per  second,  possess  ? 
(6)  What  amount  of  work  can  the  body  do  ? 

5.  (a)  What  amount  of  work  is  required  to  raise  50  tons  of  coal 
from  a  mine  200  feet  deep  ?     (6)  An  engine  of  how  many  horse-power 
would  be  required  to  do  it  in  two  hours  ? 

6.  How  many  fold  is  the  kinetic  energy  of  a  body  increased  by 
doubling  its  velocity? 

7.  Twelve  hundred  foot-pounds  of  energy  will  raise  100  pounds 
how  high,  if  none  is  wasted? 

8.  A  force  of  500  pounds  acts  upon  a  body  through  a  space  of  20 
feet.     One-fourth  of  the  work  is  wasted  in  consequence  of  resistances. 
How  much  available  energy  is  imparted  to  the  body  ? 

9.  How  much  energy  is  stored  in  a  body  weighing  1,000  pounds,  at 
a  hight  of  200  feet  above  the  earth  ? 

10.  How  much  work  can  a  2  horse-power  engine  do  in  an  hour  ? 

11.  A  horse  draws  a  carriage  on  a  level  road  at  the  uniform  rate 
of  5  miles  an  hour,     (a)  Does  work  accumulate  ?     (6)  What  kind  of 
energy  does  the  carriage  possess  ?    (c)  Suppose  that  the  carriage  were 
drawn  up  a  hill ;  would  energy  accumulate  ?   (rf)  What  kind  of  energy 
would  it  possess  when  at  rest  on  the  top  of  the  hill  ?    (e)  How  would 
you  calculate  the  quantity  of  energy  it  possesses  when  at  rest  on  top 
of  the  hill  ?    (/)  Suppose  that  the  carriage  is  in  motion  on  top  of  the 
hill;  what  two  formulas  would  you  employ  in  calculating  the  total 
energy  which  it  possesses  ? 


106  WORK  AND  ENERGY. 

Section   II. 

THE  ABSOLUTE  OR  C.G.S.  SYSTEM  OF  MEASUREMENTS. 

90.  Fundamental  Units.  —  For  many  scientific  purposes,  espe- 
cially in  establishing  a  complete  set  of  electrical  units,  a  different  system 
for  measuring  physical   quantities  than  that  in  common  use  and  called 
the  gravitation  system,  is  indispensable.     In  the  new  system,  all  physical 
quantities  may  be  expressed  in  terms  of  three  units,  which  are  called  funda- 
mental units.   All  others  are  deduced  from  these  by  definition,  and  are  called 
derived  units.    The  fundamental  units  and  their  symbols  are  as  follows:  — 

Unit  of  length,  L  :  the  centimeter,  or  the  hundredth  part  of  a  meter. 

Unit  of  mass,  M  :  the  gram,  or  the  mass  of  one  cubic  centimeter  of 
distilled  water  at  4°  C. 

Unit  of  time,  T  :  a  second. 

The  system  of  units  based  on  these  three  fundamental  units  is  called 
the  Absolute  System,  or  the  Centimeter-Gram-Second  System,  or,  by 
abbreviation,  C.G.S.  System. 

91.  Derived  Units.  —  There  are  a  great  number  of  derived  units. 
We  give  a  few  of  those  in  most  common  use. 

Unit  of  velocity,  V;  one  centimeter  per  second;  in  uniform  motion, 


Unit  of  acceleration,  A  :  an  increase  of  velocity  of  one  centimeter  per 
second. 

Unit  of  force,  F:  a  dyne;  it  is  that  force  which,  acting  for  a  second, 
will  give  to  a  mass  of  one  gram  an  acceleration  of  one  centimeter  per 
second,  i.e.  one  unit  of  acceleration.  It  is  the  -  part  of  the  weight  of  the 
unit  of  mass. 

F  =  MA  =  M^,  orMLT-2. 

Unit  of  work,  W  ;  or  of  energy,  E  :  an  erg  ;  it  is  the  work  done  or 
energy  imparted  by  a  force  of  one  dyne  working  through  a  length  or 
distance  of  one  centimeter. 

W  or  E  =  FS  -  MAS  =         ,  or 


92.  Relation  of  the  Dyne  to  the  Gram  or  Gravitation 
Unit  of  Weight.  —  When  a  body  falls  in  a  vacuum,  gravity  imparts  to 


THE  ABSOLUTE  OK  C.G.S.  SYSTEM  OF  MEASUREMENTS.     107 

it  an  acceleration  of  g  (in  the  latitude  of  the  Northern  States,  980)  centi- 
meters per  second.  The  force  of  gravity,  therefore,  acting  on  a  unit  of 
mass  is,  according  to  definition,  g  (980)  dynes.  The  weight  of  a  mass  of 
one  gram  is  in  the  gravitation  system  one  gram.  Hence  the  gram  (gravi- 
tation unit  of  weight)  must  be  equal  to  g  dynes,  or,  in  the  Northern  United 
States,  to  980  dynes.  The  weight  of  a  mass  of  one  gram  varies  with  the 
latitude  and  hight  above  the  earth's  surface,  while  the  mass  of  a  gram  and 
the  dyne  are  constant  quantities ;  their  value  does  not  change  with  place. 

93.  Another  Formula  for  Computing  Kinetic  Energy. 

—  It  is  evident  that  the  weight  of  a  body  is  dependent  upon  its  mass  and 
the  force  of  gravity ;  in  other  words,  (W  =  M#)  the  weight  of  a  body  is 
measured  by  the  product  of  the  acceleration  which  the  force  of  gravity 
produces  into  its  units  of  mass.  Hence  the  mass  of  a  body  is  numerically 

-  its  weight.  Substituting  the  value  of  W  given  above  in  the  formula 
g 

WV2  MV2 

(p.  103),  E  -          ,    we  have  E  =  =-!-.     When  the  latter  formula  is  used, 

2g  2 

it  is  evident  that  the  mass  of  the  moving  body  must  be  found  by  dividing 
its  weight  in  grams  by  980,  or  its  weight  in  pounds  by  32.1  +  . 

The  absolute  system  is  used  in  all  refined  physical  measurements, 
but  the  gravitation  system  is  more  convenient  and  is  universally  used  in 
the  ordinary  affairs  of  life. 

QUESTIONS. 

[Designed  for  only  those  who  may  take  up  the  absolute  system.] 

1.  (a.)  Name  some  unit  of  force  which  is  based  upon  the  weight  of 
some  definite  mass.     (6)  Name  some  unit  of  force  which  is  based  upon  the 
amount  of  acceleration  which  a  force  can  impart  to  a  body  of  a  given 
mass  in  a  given  time,     (c)  Have  both  of  these  units  absolute  (unchange- 
able) values  ?     (c?)  What  names  do  you  employ  in  distinguishing  these 
two  classes  of  units  ? 

2.  (a)  What   are    the    fundamental  units   of    the   absolute    system1? 
(/>)  Why  are  they  called  fundamental  units  1 

3.  A  force  of  20s  is  equivalent  to  how  many  dynes  ? 

4.  (a)  A  force  of  20  dynes  would  perform  how  many  ergs  of  work  in 
acting  through  a  distance  of  10cm  ?     (6)  How  many  ergs  of  work  would  a 
force  of  20  grams  perform  in  acting  through  the  same  distance  ?    (c)  How 
many  kilogrammeters  of  work  would  a  force  of  20  grams  perform  in  acting 
through  the  same  distance  ? 

5.  What  is  the  weight  of  a  mass  of  Is  in  dynes  ? 


108 


WORK  AND   ENERGY, 


Section  III. 


MACHINES. 

94.    Uses  of  Machines. 

Experiment  74.  —  Suspend,  as  in  Figure  95,  a  fixed  pulley,  A,  and 
a  movable  pulley,  B.  The  scale-pan  C  counterbalances  the  pulley  B, 
so  that  there  will  be  equilibrium.  Suspend  from  B  two  balls,  LL,  of 
equal  weight,  and  suspend  on  the  side  where  the  pan  is,  a  single  ball, 

K,  equal  to  one  of  the  former.  The 
single  ball  supports  the  two  balls ; 
i.e.  by  the  use  of  the  machine,  a  force 
of  1  is  enabled  to  balance  a  force  of 
2.  So  far  no  work  is  done.  (Why  ?) 
Place  a  very  small  weight  in  the  pan, 
and  the  balls  LL  begin  to  rise,  and 
work  is  done. 

As  the  weight  K  plus  a  very  small 
weight  causes  the  motion,  we  shall 
regard  this  as  the  force  (F)  ;  and  as 
the  weights  LL  are  the  bodies  moved 
(the  pulleys  and  pan  being  parts  of 
the  machine  may  be  disregarded), 
they  may  be  regarded  as  the  re- 
sistance (R)  overcome,  or  the  body 
on  which  work  is  done.  Measure 
the  respective  distances  through 
which  F  acts  and  R  moves  during 
the  same  time.  R  moves  only  one- 
half  as  great  a  distance  as  that  through  which  F  acts ;  i.e.  if  R  rises 
2  feet,  F  must  act  through  4  feet.  Suppose  that  R  is  2  pounds,  then 
F  is  1  +  pounds.  Now  2  (pounds)  X  2  feet  =  4  foot-pounds  of  work 
done  on  R.  Again,  1  +  (pounds)  x  4  feet  =  a  little  more  than  4  foot- 
pounds of  work  (or  energy)  expended. 

It  thus  seems  that,  although  a  machine  will  enable  a 
small  force  to  balance  a  large  force,  when  work  is  per- 


Fig.  95. 


MACHINES.  109 

formed,  the  work  applied  to  the  machine  is  greater,  rather 
than  less,  than  the  work  which  the  machine  transmits  to 
the  resistance.  The  work  applied  is  greater  than  the 
work  transmitted  by  the  amount  of  work  wasted  in  conse- 
quence of  friction  and  other  extra  resistances.  So  that 
by  the  employment  of  a  machine  nothing  is  gained  in  work 
which  the  force  is  required  to  do,  but  always  something  lost. 
What,  then,  is  the  advantage  gained  in  using  this 
machine?  Suppose  that  R  is  400  pounds,  and  that  the 
utmost  force  that  a  man  can  exert  is  a  little  more  than 
200  pounds.  Then,  without  the  machine,  the  services  of 
two  men  would  be  required  to  move  the  resistance ; 
whereas  one  man  can  move  it  with  a  machine,  only  that 
he  will  be  obliged  to  move  twice  as  far  as  the  resistance 
moves,  a  matter  of  little  consequence  in  comparison  with 
the  advantage  of  being  able  to  do  the  work  alone.  The 
advantage  gained  in  this  instance  seems  to  be  one  of  con- 
venience. Men,  however,  are  accustomed  to  speak  of  it  as 
"  a  gain  of  force,"  (or  more  commonly  and  inaccurately, 
"  of  power "),  inasmuch  as  a  small  force  overcomes  a 
large  resistance. 

Experiment  75.  —  If  instead  of  applying  the  small  additional 
weight  to  the  pan,  it  be  suspended  from  one  of  the  balls  LL,  the  weight 
of  these  balls,  together  with  the  additional  weight,  becomes  the  cause 
of  motion,  and  K  is  the  resistance.  In  this  case  there  is  a  loss  of 
force,  because  the  force  employed  is  more  than  twice  as  great  as  the 
force  overcome.  Measure  the  distances  traversed  respectively  by  F  and 
R  in  the  same  time.  R  moves  twice  as  far  as  F,  and  of  course  with 
twice  the  velocity.  There  is  a  gain  of  velocity  at  the  expense  of  force. 

It  thus  appears  that,  if  it  should  be  desirable  to  move  a 
resistance  with  greater  velocity  than  it  is  possible  or  con- 
venient for  the  force  to  act,  it  may  be  accomplished 
through  the  mediation  of  a  machine,  by  applying  to  it  a 


110 


WOKK   AND   ENERGY. 


force  proportionately  greater  than  the  resistance.  This 
apparatus  is  one  of  many  contrivances  called  machines, 
through  the  mediation  of  which  force  can  be  applied  to  re- 
sistance more  advantageously  than  when  it  is  applied  directly 
to  the  resistance.  Some  of  the  many  advantages  derived 
from  the  use  of  machines  are :  — 

(1)  They  may  enable  us  to  exchange  intensity  of  force 
for  velocity,  or  velocity  for  intensity  of  force.  A  gain  of  in- 
tensity of  force  or  a  gain  of  velocity  is  called  a  mechani- 
cal advantage. 


(2) 

that  is 


ance 


They  may  enable  us  to  employ  a  force  in  a  direction 
more  convenient  than  the  direction  in  which  the  resist- 
to  be  moved. 

(3)  They  may  enable  us  to  employ  other 
forces  than  our  own  in  doing  work;  e.g. 
the  strength  of  animals ;  the  forces  of  wind, 
water,  steam,  etc. 

How  are  the  last  two  uses  illustrated  in 
Figure    96  ?      The    pulleys    employed    are 
called  fixed  pulleys,  i.e.  they  have  no  motion 
except  that  of  rotation.      Is  any  mechani- 
cal   advantage    gained    by    fixed    pulleys  ? 
What  is  the  use  of  a  fixed  pulley  ?     Pulley 
B   (Fig.  94)  is  a   movable  pulley.     What 
kind  of  advantage  is  gained  by 
means  of  a  movable  pulley  ? 


Fig.  96. 


95.  General  Law  of  Machines. 

—  From  the  experiments  and  dis- 
cussion above  we  derive  the  following  formula  for  ma- 
chines :  — 

FS  =  RS'  +  w, 


MACHINES.  Ill 

in  which  F  represents  the  force  applied,  and  S  the  distance 
through  which  F  acts ;  R  represents  the  resistance  over- 
come, and  S'  the  distance  through  which  its  point  of  ap- 
plication is  moved ;  w  represents  the  wasted  work.  A 
machine  in  which  there  is  no  wasted  work  is  a  perfect 
machine.  Such  a  machine  is  purely  ideal,  as  none  exists. 
If  in  our  calculations  we  regard  a  machine  as  perfect 
(though  subsequently  suitable  allowance  must  be  made 
for  the  wasted  work),  then  our  formula  becomes 

FS  =  RS'. 

Whence  R  :  F  :  :  S  :  S' ;  i.e.  the  force  and  resistance  vary 
inversely  as  the  distances  which  their  respective  points  of  ap- 
plication move.  In  other  words,  the  ratio  of  the  resistance 
to  the  force  is  the  reciprocal  of  the  ratio  of  the  distances 
which  these  points  move. 

R  :  F  -  4,  then  S' :  S  -  J. 

This  law  applies  to  every  machine  of  whatever  descrip- 
tion ;  hence  it  is  called  the  G-eneral  or  Universal  Law  of 
Machines.  When  R  is  greater  than  F,  there  is  a  gain  of 

Tt 

force,   and  —  ==  the  ratio   of  gain  of  force.     When  S'  is 

g/ 

greater  than  S,  there  is  a  gain  of  velocity,  and  TT  =  the 
ratio  of  gain  of  velocity. 

Experiment  76.  —  Support  a  lever,  as  in  Figure  97,  so  that  there 
shall  be  unequal  arms.  Move  w  until  the  lever  is  balanced  in  a  hori- 
zontal position.  Suspend  (say) 
seven  balls  from  the  short  arm 
(say)  one  space  from  the  ful- 
crum. Then  from  the  other 
arm  suspend  a  single  ball  from 
such  a  place  (in  this  case  seven 
equal  spaces  from  the  fulcrum) 
that  it  will  balance  the  seven 
balls.  There  is  now  equilibrium  between  the  two  forces.  Suppose 


112 


WORK  AND   ENERGY. 


the  smaller  force  to  be  increased  a  little  and  to  produce  motion  ;  what 
mechanical  advantage  (i.e.  intensity  of  force  or  velocity)  would  be 
gained  by  the  use  of  the  machine  ?  What  is  the  ratio  of  gain  neg- 
lecting the  small  additional  force?  How  does  this  ratio  compare  with 
the  ratio  between  the  length  of  the  two  arms  ?  For  convenience  we 
call  the  distance  of  the  point  of  application  of  the  force  from  the 
fulcrum  the  force-arm,  and  the  distance  of  the  resistance  from  the 
fulcrum  the  resistance-arm. 

Suppose  the  small  additional  force  is  applied  to  the  short  arm; 
what  mechanical  advantage  would  be  gained?  What  would  be  the 
ratio  of  gain  ? 

While  the  general  law  of  machines  is  always  applica- 
ble, a  special  law,  one  in 
which  the  relation  be- 
tween the  ratio  of  gain 
and  the  ratio  between 
certain  dimensions  of 
the  machine  is  stated,  is 
often  more  convenient  in 
practice.  For  example, 
in  our  experiment  with 
the  lever  we  discover 
that  R :  F : :  force-arm  : 
resistance-arm,  i.e.  the 
force  and  resistance  vary 
inversely  as  the  lengths 
of  their  respective  arms. 
Compare  this  special  law 
with  the  general  law. 
Place  the  fulcrum  at  other  points  in  the  lever,  and  thereby 
vary  the  length  of  the  arms,  and  verify  by  numerous 
experiments  the  special  law  of  levers. 

Experiment  77.  —  By  means  of  a  pulley,  D,  so  arrange  (Fig.  98) 
that  both  F  and  R  may  be  on  the  same  side  of  the  fulcrum.  First, 


Fig.  98. 


MACHINES. 


113 


place  in  the  pan  weights  sufficient  to  produce  equilibrium  in  the 
machine  (for  example,  in  this  case,  one  ball).  Then  suspend  weights 
at  some  point,  as  A,  and  place  other  weights  in  the  pan  to  counter- 
balance these.  Verify  the  law  of  levers.  If  A  is  the  resistance,  what 
mechanical  advantage  is  gained  ?  What  is  the  ratio  of  gain  ?  If  B 
is  the  resistance,  what  mechanical  advantage  will  be  gained  ? 

Experiment  78. — Obtain 
a  toy  carriage,  place  it  on  an 
inclined  plane,  pass  the  cord 
over  a  pulley,  B  (Fig.  99), 
so  adjusted  that  the  cord 
between  the  carriage  and 
pulley  shall  be  parallel  with 
the  plane.  Suspend  a  small 
bucket,  P,  and  place  sand  in 
it  to  balance  the  carriage. 
Place  in  the  carriage  a  weight  W,  and  place  weights  in  the  bucket  to 
balance  W.  The  weights  placed  in  the  bucket  represent  the  force 


Fig.  99. 


Fig.  10O.  Fig.  101. 

applied ;  then  what  advantage  is  gained  in  the  use  of  an  inclined  plane 
as  a  machine?  W,  in  traversing  the  inclined  plane  AB,  only  rises 
through  the  vertical  hight  CB,  while  P  must  move  through  a  distance 
equal  to  AB.  Measure  the  distances  AB  and  CB.  How  does  the  ratio 


114 


WOKK  AND  ENERGY. 


between  these  distances  compare  with  the  ratio  of  gain?    Construct  a 
special  law  of  the  inclined  plane. 

Experiment  79.  — Place  a  "wheel  and  axle"  (Fig.  100)  on  the 
support  A.  Wind  a  cord  around  the  wheel  B,  and  another  in  the  re- 
verse direction  around  the  axle  C.  Suspend  a  weight,  D,  from  the 
axle,  and  another,  E,  from  the  wheel,  to  balance  it.  If  E  be  the 
force  applied,  what  advantage  is  gained  ?  What,  if  D  is  the  force 
applied  ?  What  is  the  ratio  of  advantage  in  either  case  ?  How  does 
the  ratio  of  advantage  compare  with  the  ratio  between  the  radius  of 
the  wheel  AC  (Fig.  101)  and  the  radius  of  the  axle  BC  ?  Construct  a 
special  law  of  the  wheel  and  axle  . 


Fig.  102. 
EXERCISES. 


1.  (a)  When  is  a  machine  said  to  gain  intensity  of  force?   (&)  When 
is  it  said  to  gain  velocity  ? 


MACHINES. 


115 


Fig.  104. 


2.  (a)  Can  any  machine  do  work  ?     (6)  Can  we  by  the  use  of  any 
machine  accomplish  more  work  than  the  work  performed  upon  the 
machine  ?    What  is  the  proof  ? 

3.  How  is    intensity  of    force 
gained  by  the  use  of  a  machine  ? 

4.  What  machine  is  used  only 
to  change  the  direction  of  motion  ? 

c     ,  °     TirT,     ..  i        •      ,  Fig'  1O3. 

5.  (a)  What  is  a  mechanical 

advantage?      (b)  Give  a  rule  by  which   the  mechanical   advantage 
that  may  be  gained  by  any  machine  may  be  calculated. 

6.  Figure  102  repre- 
sents a  pile-driver,  (a) 
How  can  the  energy  or 
the  work  which  the  weight 
W  can  do  when  it  is  raised 
a  given  distance  be  com- 
puted ?  (b)  What  benefit  is  derived  from  the  use  of  the  machine  in 
raising  the  weight?  (c)  Suggest  some  simple  attachment  to  the 
machine  which  would  enable  one  man  to  raise  the  weight.  («?)  Sug- 
gest some  attachment  by  means  of  which  a  horse  could  be  made  to  do 
the  work,  (e)  What 
difference  will  it  make 
whether  the  weight  is 
raised  5  feet  or  10 
feet?  (/)  Illustrate, 
by  means  of  this  ma- 
chine, what  you  un- 
derstand by  force  and 
energy.  (g)  Which, 
while  the  weight  rises, 
is  constantly  accumu- 
lating, and  which  re- 
mains nearly  constant  ? 
(A)  Which  can  be  meas-  Fig*  106' 

ured  with  an  instrument,  and  what  is  the  name  of  the  instrument? 

7.  (a)  What  advantage  is  gained  by  a  lever  when  its  force-arm  is 
longer  than  its  resistance-arm  ?     (b)  What,  when  its  resistance-arm  is 
longer  ? 

8.  (a)  What  advantage  is   gained  by  a  nut-cracker  (Fig.  103)? 
(&)  What  is  the  ratio  of  gain?. 


116 


WORK  AND   ENERGY. 


Fig.  1O6. 


9.  (a)  What  advantage  is  gained  by  cutting  far  back  on  the  blades 
of  shears  near  the  fulcrum?  Why?  (6)  Should  shears  for  cutting 
metals  be  made  with  short  handles  and  long  blades,  or  the  reverse  ? 
(c)  What  is  the  advantage  of  long  blades  ? 

10.  Is  work  done  when  the 
moment  of  the   force  applied 
to  a  lever  is  equal  to  the  mo- 
ment of  the  resistance  ?  Why  ? 

11.  (a)    If    P   (Fig.    105), 
weighing  1  pound,  is  suspend- 
ed 15  spaces  from  the  fulcrum 
of  the  steelyard,  what  weight 
(W),    suspended     3     similar 
spaces  the    other  side  of  the 
fulcrum,  will  balance  it?    (6) 

Where  would  you  place  the  one-pound  weight  in  order  to  weigh  out 
6  pounds  of  tea  ? 

12.  (a)  If  the  circumference  of  the  axle  (Fig.  106)  is  15  inches, 
and  the  force  applied  to  the  crank  acts  through  15  feet  during  each  rev- 
olution, what  force  will  be  necessary 

to  raise  the  bucket  of  coal  weighing 
(say)  36  pounds  ?  (&)  Through  how 
many  feet  must  the  force  act  to  raise 
the  bucket  from  a  cavity  48  feet 
deep? 

13.  The  arm  is  raised  by  the  con- 
traction   (shortening    by    muscular 
force)  of  the  muscle  A  (Fig.  107), 
which  is  attached  at  one  extremity 
to  the  shoulder  and  at  the  other  ex- 
tremity B  to  the  fore-arm,  near  the 

elbow,  (a)  When  the  arm  is  used,  as  represented  in  the  figure,  to 
raise  a  weight,  what  kind  of  a  machine  is  it  ?  (£)  What  mechanical 
advantage  is  gained  by  it  ?  (c)  How  can  the  ratio  of  gain  be  com- 
puted ?  (e?)  For  which  purpose  is  the  arm  adapted,  to  gain  intensity 
of  force  or  velocity  ? 

The  lengths  of  the  two  arms  of  a  balance,  such  as  is  used  in  finding 
specific  gravity  (Fig.  60,  page  61),  should  be  exactly  equal.  The  arms 
may  be  of  unequal  length,  and  yet  the  beam  may  be  in  equilibrium 


Fig.  107. 


MACHINES. 


117 


(i.e.  take  a  horizontal  position  when  no  weights  are  applied),  in  conse- 
quence of  having  more  matter  in  the  shorter  arm,  as  in  Figure  97,  page 
111.  Such  a  balance  is  called  a,  false  balance. 

14.  (a)  How  would  you  test  a  balance  to  ascertain  whether  it  is 
true  or  false  ?  (&)  If  you  were  buying  diamonds,  and  the  seller  should 
sell  them  to  you  by  weight  as  obtained  by  placing  them  on  the  shorter 
arm  of  a  false  balance,  would  you  be  the  loser  or  gainer  ? 

The  true  weight  of  a  body  may  be  found  with  a  false  balance  by  a 
process  called  double  weighing.  The  article  to  be  weighed  is  placed  in  one 
pan,  and  a  counterpoise  of  sand  in  the  other  pan.  The  article  is  then 
removed,  and  known  weights  placed  in  the  pan  until  equilibrium  is  again 
produced.  These  weights  represent  the  correct  weight  of  the  article.  In 
this  way  the  balances  used  in  the  school  laboratory  should  be  tested  by 
the  pupil. 


Fig.  108. 


Fig.  109. 


15.  During  one  revolution   a  screw  advances  a  distance  equal  to 
the  distance  between  two  threads,  measured  in  the  direction  of  the 
axis  of  the  screw.     Suppose  the  screw  in  the  letter-press  (Fig.  108)  to 
advance  \  inch  at  each  revolution,  and  a  force  of  25  pounds  to  be 
applied  to  the  circumference  of  the  wheel  B,  whose  diameter  is  14 
inches.     What  pressure  would  be  exerted  on  articles  placed  beneath 
the  screw?     (The  circumference  of  a  circle  is  3.1416  times  its  diame- 
ter.) 

16.  The  toggle-joint  (Fig.  109)  is  a  machine  employed  where  great 
pressure  has  to  be  exerted  through  a  small  space,  as  in  punching  and 


118 


WORK  AND   ENERGY. 


Fig.  110. 


shearing  iron,  and  in  printing-presses,  in  pressing  the  types  forcibly 
against  the  paper.  An  illustration 
maybe  found  in  the  joints  used  to 
raise  carriage-tops.  Force  applied 
to  the  joint  C  will  cause  the  two 
links  AC  and  BC  to  be  straight- 
ened, or  carried  forward  to  e.  If 
point  C  moves  5  inches  while  G 
moves  i  inch,  then  what  pressure 
will  a  force  of  50  pounds  applied 
at  C  exert  on  the  book  below*?  - 

17.  Show  that  the  hydrostatic 
press  (page  50)  conforms  in  its 
operation  to  the  general  law  of  machines. 

18.  A  wedge  may  be  regarded  as  two  inclined 
planes  placed  base  to  base,  as  dc  (Fig.  110). 
(a)  What  mechanical  advantage  is  gained  by  it  ? 
(6)  Suppose  that  the  thickness  db  is  4  inches, 
and  the  length  dc  is  8  inches,  and  that  the  aver- 
age pressure  exerted  upon  it  by  the  blow  of  a 
sledge  is  100  pounds ;  what  will  be  the  average 
pressure  exerted  by  the  wedge  tending  to  separate 
the  fibers  of  wood? 

A  compound  machine  is  one  consisting  of  two  or  more  machines 

combined  in  one;  e.g.  com- 
pound pulleys  (Fig.  Ill)  and 
compound  wheels  and  axles 
(Fig.  112).  The  mechanical 
advantage  that  may  be  gained 
by  a  compound  machine  may 
be  calculated  by  multiplying 
continuously  together  the  ra- 
tios of  the  several  machines. 

19.  (a)    How  great  is  the 
advantage  gained  by  one  mov- 
able pulley?  (J)  How  great  is 
the  advantage  gained  by  the 
Fig.  ii3.  compound  pulley   (Fig.   Ill) 

consisting  of  three  movable  pulleys? 


MACHINES. 


119 


20.  Suppose  that  the  radii  of  the  wheels  a,  d,  and/  (Fig.  112)  are, 
respectively,  20  inches,  16  inches,  and  24  inches,  and  the  radii  of  their 
axles  are,  respectively,  2  inches,  4  inches,  and  6  inches;  how  great 
advantage  may  be  gained  by  the  compound  machine? 


Fig.  113. 


Fig.  114. 


21.  How  would  you  calculate  the  mechanical  advantage  gained  by 
a  machine  like  that  of  Figure  113  ?    (On  the  axle  A  is  an  endless  screw, 
by  means  of  which  motion  is  communicated  from  the  axle  to  the 
wheel  W.) 

22.  (a)  What  kind  of  a  machine  is  a  claw-hammer  (Fig.  114)  ? 
(&)  What  mechanical  advantage  is  gained  by  it  ? 

23.  In  its  technical  meaning,  a  "  perpetual  motion  machine  w  is  not 
a  machine  that  will  run  indefinitely,  but  a  machine  which  can  do  work 
without  the  expenditure  of  energy.     Is  such  a  machine  possible? 

24.  A  plank  12  feet  long  and  weighing  24  pounds  is  supported  by 
two  props,  one  3  feet  from  one  end,  and  the  other  1  foot  from  the 
other  end.     What  is  the  pressure  on  each  prop? 

%    25.  With  a  movable  pulley  what  force  will  support  a  weight  of 
100  pounds  ? 

26.  The  gradient  of  a  certain  road  on  a  hillside  is  one  foot  in  ten 
feet.     What  force  must  a  horse  exert  on  a  carriage  which  weighs  to- 
gether with  its  load  one  ton,  to  prevent  its  descent  ? 

27.  What  must  be  the  diameter  of  a  wheel  in  order  that  a  force  of 
20  pounds  applied  at  its  circumference  may  be  in  equilibrium  with  a 
resistance  of  600  pounds  applied  to  its  axle,  which  is  3  inches  in  diam- 
eter? 


120 


WORK    AND    ENERGY. 


28.  Draw  a  straight  line  to  represent  a  lever ;  locate  the  fulcrum, 
and  locate  the  points  of  application  of  the  force  and  resistance  un- 
equally distant  from  the  fulcrum.  Draw  lines  from  the  points  of 
application  of  the  force  and  resistance  so  that  they  will  make  some 
angle  with  each  other  (i.e.  not  parallel  with  each  other)  to  represent 
the  directions  in  which  the  two  forces  respectively  act.  Ascertain  the 
ratio  between  the  twoforces  when  their  moments  are  equal,  i.e.  when 
the 


CHAPTER  V. 
MOLECULAR   ENERGY.  — HEAT. 

Section  I. 

WHAT   HEAT  IS. — SOME   SOURCES   OF   HEAT. 

96.  Theory  of  Heat.  —  A  body  loses  motion  in  com- 
municating it.  The  hammer  descends  and  ""Strikes  the 
anvil;  its  motion  ceases,  but  the  anvil  is  not  sensibly 
moved ;  the  only  observable  effect  produced  is  heat.  In- 
stead of  a  motion  of  the  hammer  and  anvil,  there  is  now, 
according  to  the  modern  view,  an  increased  vibratory  mo- 
tion of  the  molecules  that  compose  the  hammer  and  anvil, 
—  simply  a  change  from  molar  to  molecular  motion.  Of 
course,  this  latter  motion  is  invisible.  According  to  this 
view,  heat  is  but  a  name  for  the  energy  of  vibration  'of  the 
molecules  of  a  body.  A  body  is  heated  by  having  the 
motion  of  its  molecules  quickened,  and  cooled  by  parting 
with  some  of  its  molecular  motion.  One  body  is  hotter 
than  another  when  the  average  kinetic  energy  of  each  mole- 
cule in  it  is  greater  than  in  the  other. 

As  late  as  the  beginning  of  the  present  century  heat  was  generally 
regarded  as  "  a  sensation  which  the  presence  of  fire  "  (an  "  igneous  fluid," 
"  matter  of  heat,"  called  sometimes  "  caloric  ")  "  occasions  in  animate  and 
inanimate  bodies."  A  text-book  of  that  period  makes  this  significant 
statement :  "There  is  fire  in  the  wood,  and  there  is  air  in  the  field,  though 
we  do  not  perceive  either  while  at  rest.  Rubbing  two  pieces  of  wood  does 
not  create  fire  any  more  than  the  blowing  of  the  wind  creates  air.  Motion 
renders  both  perceptible."  The  former  and  the  more  modern  views  are  in 


122  MOLECULAR   ENERGY.  —  HEAT. 

harmony  in  attributing  the  immediate  cause  of  the  sensation  to  motion. 
According  to  the  former  view,  the  sensation  is  produced  by  putting  an 
imaginary  fluid  in  motion ;  according  to  the  modern  view  it  is  produced  by 
quickening  the  motion  of  the  molecules  of  a  body. 

97.  Artificial  Sources  of  Heat.  —  As  heat  is  energy, 
so  all  heat  must  originate  in  some  form  of  energy,  i.e.  by 
the  transformation  of  some  other  form  of  energy  into  heat. 

Experiment  80.  —  Place  a  ten-penny  nail  on  a  stone  or  a  flat 
piece  of  iron  and  hammer  it  briskly  for  a  few  minutes.  It  soon  be- 
comes too  hot  to  be  handled  with  comfort.  Rub  a  desk  with  your  fist ; 
your  coat-sleeve  with  a  metallic  button;  both  the  rubbers  and  the 
things  rubbed  become  heated. 

(1)  Heat  is  generated  at  the  expense  of  molar  motion, 
i.e.  molar  motion  checked  becomes  molecular  motion,  or  heat. 

Experiment  81.  —  Take  a  glass  test-tube  half  full  of  cold  water 
and  pour  into  it  one-fourth  its  volume  of  strong  sulphuric  acid.  The 
liquid  almost  instantly  becomes  so  hot  that  the  tube  cannot  be  held  in 
the  hand. 

When  water  is  poured  upon  quicklime,  heat  is  rapidly 
developed.  The  invisible  oxygen  of  the  air  combines  with 
the  constituents  of  the  various  fuels,  such  as  wood,  coal, 
oils,  and  illuminating-gas,  and  gives  rise  to  what  we  call 
burning,  or  combustion,  by  which  a  large  amount  of  heat  is 
generated.  In  all  such  cases  the  heat  is  generated  by  the 
combination  or  clashing  together  of  molecules  of  sub- 
stances that  have  an  affinity  (i.e.  an  attraction)  for  one 
another.  Before  union  the  energy  of  the  molecules  is  of 
the  same  kind  as  that  of  a  stone  on  a  shelf.  When  the 
shelf  is  withdrawn,  gravity  converts  the  potential  energy 
of  the  stone  into  kinetic  energy ;  so  affinity  converts  the 
potential  energy  of  the  molecules  into  kinetic  energy 
of  vibration ;  i.e.  into  heat. 


WHAT  HEAT   IS.  123 

(2)  Molecular  (or  atomic)  potential  energy  is  transformed 
in  the  act  of  chemical  combination  into  heat. 

98.    The  Sun  as  a  Source  of  Heat  and  Energy.  —  The 

sun  is  the  source  of  very  nearly  all  the  energy  employed  by 
man  in  doing  work.  Our  coal-beds,  the  results  of  the  de- 
posit of  vegetable  matter,  are  vast  storehouses  of  the  sun's 
energy,  rendered  potential  during  the  growth  of  the  plants 
many  ages  ago.  The  animal  finds  its  food  in  the  plant, 
appropriates  the  energy  stored  in  the  plant,  and  converts 
it  into  energy  of  motion  in  the  form  of  animal  heat  and 
muscular  motion.  Every  rain-drop  that  rolls  its  way  to  the 
sea,  contributing  its  mite  to  the  immense  water-power  of 
the  earth,  derives  its  energy  from  the  sun. 

QUESTIONS. 

1.  On  every  hand  we  see  what  appears  to  be  at  least  an  almost 
universal  tendency  to   destruction   of   motion.  '    Is  the   destruction 
usually  an  annihilation  of  motion  ? 

2.  What  name  is  usually  given  to  molecular  energy? 

3.  How  does  it  appear  that  heat  is  energy? 

4.  What  do  you  mean  when  you  say  that  one  body  is  hotter  than 
another  ? 

5.  How  must  all  heat  originate  ? 

6.  State  all  the  sources  of  heat  with  which  you  are  now  acquainted. 

7.  (a)  Give  an  illustration  of  mechanical  or  visible  motion  trans- 
formed into  molecular  motion,     (b)  Give  an  illustration  of  molecular 
motion  transformed  into  mechanical  motion. 

8.  What  kind  of  energy  does  coal  and  other  fuel  possess  ? 

9.  A  lump  of  coal  is  raised  and  placed  upon  a  shelf,     (a)  How  can 
the  potential  energy  of  the  lump  be  transformed  into  kinetic  energy  ? 
(&)  Will  the  kinetic   energy  resulting  from  the  transformation   be 
mechanical  or  molecular  ?     (c)  When  the  lump  strikes  the  earth,  what 
transformation  of  energy  occurs  ? 

10.  Every  lump  of  coal  possesses  molecular  potential  energy,     (a) 
How  can  its  energy  be  transformed  into  kinetic  energy  ?     (6)  What 


124  MOLECULAR    ENERGY.  —  HEAT. 

two  varieties  of  potential  energy  does  a  lump  of  coal  on  the  shelf 
possess  ? 

11.  (a)  How  do  bodies  acquire  energy?     (&)  From  what  source  did 
coal  obtain  its  molecular  potential  energy  ?     (c)  What  does  the  entire 
value  of  coal  consist  in  ? 

12.  How  does  animal  energy  originate? 


Section  II. 

TEMPERATURE.  —  METHODS   OF   EQUALIZATION. 

99.  Temperature    Defined.  —  If   body  A   is   brought 
in    contact  with   body  B,  and    A   tends   to   impart   heat 
to  B,  then  A  is  said  to  have  a  higher  temperature  than 
B.      Temperature  is  the  state  of  a  body  with  reference  to 
its  tendency  to  communicate  heat  to,  or  receive  heat  from, 
other  bodies.      The  direction  of  the  flow  of  heat  deter- 
mines which  of  two  bodies  has  the  higher  temperature. 
If  the  temperature  of  neither  body  rises  at  the  expense 
of  the  other,  then  both  have  the  same  temperature. 

100.  Temperature  distinguished  from  Quantity  of 
Heat.  —  The  term  temperature  does  not  signify  quantity 
of  heat.     If  we  dip  from  a  gallon  of  boiling  water  a  cupful, 
the  cup  of  water  is  just  as  hot,  i.e.  has  the  same  tempera- 
ture, as  the  larger  quantity,  although  of  course  there  is  a 
great  difference  in  the  quantities  of  heat  the  two  bodies  of 
water  contain.     Temperature  depends  upon  the  average  ki- 
netic energy  of  the  individual  molecule,  while  quantity  of 
heat  depends  upon  the  average  kinetic  energy  of  the  indi- 
vidual molecule  multiplied  by  the  number  of  molecules. 


TEMPERATURE.  —  METHODS   OF   EQUALIZATION.      125 

There  is  always  a  tendency  to  equalization  of  tempera- 
ture; that  is,  heat  has  a  tendency  to  pass  from  a  warmer 
body  to  a  colder,  or  from  a  warmer  to  a  colder  part  of  the 
same  body,  until  there  is  an  equality  of  temperature. 

1O1.    Conduction. 

Experiment  82.  —  Place  one  end  of  a  wire  about  10  inches  long 
in  a  lamp-flame,  and  hold  the  other  end  in  the  hand.  Heat  gradually 
travels  from  the  end  in  the  flame  toward  the  hand.  Apply  your  fin- 
gers successively  at  different  points  nearer  and  nearer  the  flame ;  you 
find  that  the  nearer  you  approach  the  flame,  the  hotter  the  wire  is. 

The  flow  of  heat  through  an  unequally  heated  body, 
from  places  of  higher  to  places  of  lower  temperature,  is 
called  conduction  ;  the  body  through  which  it  travels  is 
called  a  conductor.  The  molecules  of  the  wire  in  the  flame 
have  their  motion  quickened ;  they  strike  their  neighbors 
and  quicken  their  motion ;  the  latter  in  turn  quicken  the 
motion  of  the  next ;  and  so  on,  until  some  of  the  motion 
is  finally  communicated  to  the  hand,  and  creates  in  it  the 
sensation  of  heat. 

Experiment  83.  —  Figure  115  represents  a  board  on  which  are 
fastened,  by  means  of  staples,  four  wires :  (1) 
iron,  (2)  copper,  (3)  brass,  and  (4)  German 
silver.  Place  a  lamp-flame  where  the  wires  meet. 
In  about  a  minute  run  your  fingers  along  the 
wires  from  the  remote  ends  toward  the  flame, 
and  see  how  near  you  can  approach  the  flame  on 
each  without  suffering  from  the  heat.  Make  a 
list  of  these  metals,  arranging  them  in  the  order  Fis-  116- 

of  their  conductibility. 

You  learn  that  some  substances  conduct  heat  much  more 
rapidly  than  others.  The  former  are  called  good  conduc- 
tors, the  latter  poor  conductors.  Metals  are  the  best  con- 
ductors, though  they  differ  widely  among  themselves. 


126 


MOLECULAR  ENERGY.  —  HEAT. 


Experiment  84.  —  Fill  a  test-tube  full  of  water,  and  hold  it  some- 
what inclined  (Fig.  116),  so  that  a  flame  may  heat  the  part  of  the 
tube  near  the  surface  of  the  water.  Do 
not  allow  the  flame  to  touch  the  part  of 
the  tube  that  does  not  contain  water. 
The  water  may  be  made  to  boil  near  its 
surface  for  several  minutes  before  any 
change  of  the  temperature  at  the  bottom 
will  be  perceived. 

Liquids,  as   a   class,  are  poorer 
conductors  than  solids.     Gases  are 
Fig.  no.  much  poorer  conductors  than  liquids. 

It  is  difficult  to  discover  that  pure,  dry  air  possesses  any 
conducting  power.  The  poor  conducting  power  of  our 
clothing  is  due  partly  to  the  poor  conducting  power  of 
the  fibers  of  the  cloth,  but  chiefly  to  the  air  which  is 
confined  by  it. 

Loose  garments,  and  garments  of  loosely  woven  cloth,  inasmuch  as 
they  hold  a  large  amount  of  confined  air,  furnish  a  good  protection  from 
heat  and  cold.  Bodies  are  surrounded  with  bad  conductors,  to  retain  heat 
when  their  temperature  is  above  that  of  surrounding  objects,  and  to 
exclude  it  when  their  temperature  is  below  that  of  surrounding  objects. 
In  the  same  manner  double  windows  and  doors  protect  from  cold. 


1O2.    Convection  in  Gases. 

Experiment  85.  —  Hold  your  hand  a  little  way 
from  a  flame,  beneath,  on  the  side  of,  and  above  the 
flame.  At  which  place  is  the  heat  most  intense  ? 

Experiment  86.  —  DrawT  on  thin  glazed  paper 
an  unfolding  line,  so  that  the  windings  shall  be 
about  f  inch  apart.  Cut  along  the  line;  give  the 
central  portion  a  conical  form ;  place  the  cone  on 
a  pointed  end  of  a  vertical  wire,  and  allow  the 
remainder  of  the  paper  to  fall  spirally  around  the 
wire  as  in  Figure  117.  Place  the  spiral  over  a  flame 
or  hot  stove.  A  continuous  current  of  air,  a  mini- 


Fig.  117. 


ature  wind,  moving  upward  from  the  flame  or  stove  causes  the  spiral 


TEMPERATURE.  —  METHODS   OF   EQUALIZATION.     127 

to  rotate.  This  current  tends  only  upward.  The  air  having  become 
heated  by  contact  with  the  surfaces  of  the  flame  or  stove  conveys,  in 
its  ascent,  heat  to  objects  above.  Heat  is  thus  diffused  by  a  process 
called  convection  (conveying). 

Experiment  87.  —  Cover  a  candle-flame  with  a  glass  chimney  (Fig. 
118),  blocking  the  latter  up  a  little  way  so  that  there  may  be  a  circu- 
lation of  air  beneath.  Hold  the  spiral  over  the  chimney ;  the  rotation 
is  much  quicker  than  before.  Hold  smoking  touch-paper  near  the 
bottom  of  the  chimney;  the  smoke  seems  to  be  drawn  with  great 
rapidity  into  the  chimney  at  the  bottom ;  in  other  words,  the  office  of 
the  chimney  is  to  create  what  is  called  a  draft  of  air.  Notice  whether 
the  combustion  takes  place  any  more  rapidly  with  than  without  the 
chimney. 


Fig.  118.  Fig.  119. 

Experiment  88.  —  Place  a  candle  within  a  circle  of  holes  cut  in  the 
cover  of  a  vessel,  and  cover  it  with  a  chimney,  A  (Fig.  119).  Over 
an  orifice  in  the  cover  place  another  chimney,  B.  Hold  a  roll  of 
smoking  touch-paper  over  B.  The  smoke  descends  this  chimney, 
passes  through  the  vessel  and  out  at  A.  This  illustrates  the  method 
often  adopted  to  produce  a  ventilating  draft  through  mines.  Let  the 
interior  of  a  tin  vessel  represent  a  mine  deep  in  the  earth,  and  the 
chimneys  two  shafts  sunk  to  opposite  extremities  of  the  mine.  A  fire 
kept  burning  at  the  bottom  of  one  shaft  will  cause  a  current  of  air 


128 


MOLECULAR  ENERGY.  —  HEAT. 


to  sweep  down  the  other  shaft,  and  through  the  mine,  and  thus  keep 
up  a  circulation  of  pure  air  through  the  mine. 

The  cause  of  the  ascending  currents  is  evident.  Air,  on  becoming 
heated,  expands  rapidly  and  becomes  much  rarer  than  the  surround- 
ing colder  air ;  hence  it  rises  much  like  a  cork  in  water,  while  cold 
air  pours  in  laterally  to  take  its  place.  In  this  manner  winds  are 
created. 

The  so-called  trade-winds  originate  in  the  torrid  or  heated  zone  of  the 
earth.  The  air  over  the  heated  surface  of  the  earth  rises,  and  the  colder 
air  from  the  polar  regions  flows  in  on  both  sides,  giving  rise  to  a  constant 
southward  wind  in  the  northern  hemisphere,  and  northward  wind  in  the 
southern  hemisphere. 

Chemistry  teaches  us  the  vital 
importance  of  thorough  ventilation. 
Figure  120  represents  a  scheme  for 
heating  a  room  by  steam,  and  venti- 
lating it  by  convection.  Steam  is 
conveyed  by  a  pipe  from  the  boiler 
to  a  radiator  box  just  beneath  the 
floor  of  the  room.  The  air  in  the 
box  becomes  heated  by  contact  with 
and  radiation  from  the  coil  of  pipe 
in  the  box,  and  rises  through  a  pas- 
sage opening  by  means  of  a  register 
into  the  room  near  the  floor  at  C,  a 
supply  of  pure  air  being  kept  up  by 
means  of  a  tubular  passage  opening 
into  the  box  from  the  outside  of 
the  building.  Thus  the  room  is  fur- 
nished with  pure  warm  air,  which, 
mingling  with  the  impurities  aris- 
ing from  the  respiration  of  its  occu- 
pants, serves  to  dilute  them,  and 
render  them  less  injurious.  At  the 
same  time,  the  warm  and  partially 
Fig.  120.  vitiated  air  of  the  room  passes 

through  the  open  ventilator,  A,  into  the  ventilating-flue,  and  escapes,  so 
that  in  a  moderate  length  of  time  a  nearly  complete  change  of  air  is 
effected.  It  is  evident  that  on  the  coldest  days  of  winter  the  convection 
is  most  rapid ;  indeed,  it  may  be  so  rapid  that  the  air  cannot  be  heated 
sufficiently  to  render  the  room  near  the  floor  comfortable.  At  such  times 


TEMPERATURE. — METHODS   OF  EQUALIZATION.     129 

the  ventilator  A  may  be  closed,  while  the  ventilator  B  is  always  open. 
The  heated  air  rises  to  top  of  the  room  and,  not  being  able  to  escape, 
crowds  the  colder  air  beneath  out  at  the  ventilator  B.  No  system  of 
ventilation  dependent  wholly  on  convection  is  adequate  to  ventilate 
properly  crowded  halls ;  air  is  too  viscous  and  sluggish  in  its  movements. 
In  such  cases  ventilation  should  be  assisted  by  some  mechanical  means, 
such  as  a  blower  or  fan,  worked  by  steam  or  water  power. 

103.  Convection  in  Liquids. 

Experiment  89.  —  Fill  a  small  (6  ounce),  thin  glass  flask  with 
boiling  hot  water,  color  it  with  a  teaspoonful  of  ink,  stopper  the  flask, 
and  lower  it  deep  in  a  tub,  pail,  or  other  large  vessel  filled  with  cold 
water.  Withdraw  the  stopper,  and  the  hot,  rarer,  colored  water  will 
rise  from  the  flask,  and  the  cold  water  will  descend  into  the  flask. 
The  two  currents  passing  in  and  out  of  the  neck  of  the  flask  are  easily 
distinguished.  The  colored  liquid  marks  distinctly  the  path  of  the 
heated  convection  currents  through  the  colored  liquid  and  makes  clear 
the  method  by  which  heat,  when  applied  at  the  bottom  of  a  body  of 
liquid,  becomes  rapidly  diffused  through  the  entire  mass  notwithstand- 
ing that  liquids  are  poor  conductors. 

Experiment  90.  —  Fill  again  the  flask  with  hot  colored  water, 
stopper,  invert,  and  introduce  the  mouth  of  the  flask  just  beneath  the 
surface  of  a  fresh  pail  of  cold  water.  Withdraw  the  stopper  with  as 
little  agitation  of  the  water  as  possible.  What  happens?  Explain. 

104.  Radiation.  —  In  some  way  the  sun  is  the  cause 
of  a  large  amount  of  the  heat  which  the  surface  of  the 
earth  possesses.     On  the  other  hand,  the  earth  in  some 
way   parts   with  a  large    amount  of   heat.      It   is   quite 
apparent  that  the  earth  does  not  receive  heat  from  the 
sun  by  conduction   or   convection,    and   that   by  neither 
of   these   processes   does  it  part  with   heat.      It  is  also 
apparent  that  there  is  another  and  a  much  more  rapid 
and  effectual  method  by  which  bodies  of  higher  tempera- 
ture on  the  earth  part  with  their  heat,  and  other  bodies  of 
lower  temperature  acquire  heat  at  the  expense  of  distant 
bodies,  than  by  either  of  the  two  comparatively  slow  pro- 
cesses of  diffusion  so  far  described.     This  process  is  called 


130  MOLECULAR  ENERGY.  —  HEAT. 

radiation.  The  process  is  a  very  peculiar  one,  and  must 
be  reserved  for  discussion  in  its  proper  place  in  the  chapter 
on  Radiant  Energy. 

QUESTIONS. 

1.  Why  does  more  heat  reach  your  hand  above  than  at  an  equal 
distance  beside  a  flame  ? 

2.  Why  is  loose  clothing  warmer  than  tight-fitting  clothing? 

3.  (a)  Which  contains  more  heat,  the  Atlantic  Ocean  or  a  tea-kettle 
full  of  boiling  water?     (&)  Which  is  capable  of  giving  heat  to  the 
other?    (c)  Can  a  body  have  less  heat  than  another  and  yet  be  hotter 
than  the  other? 

4.  Why  should  heat  be  applied  to  the  bottom  of  a  body  of  water? 

5.  (a)  How  is  equalization  of  temperature  effected  in  solids?    (6)  In 
liquids  and  gases  ? 


Section  III. 

EFFECTS  OF  HEAT.  —  EXPANSION. 

1O5.   Expansion  of  Solids,  Liquids,  and  Gases. 

Experiment  91.  —  The  brass  ring  and  ball  (Fig.  121)  are  so 
constructed  that  the  latter  will  just  pass  through 
the  former  when  both  have  the  same,  or  nearly  the 
same,  temperature.  Heat  the  ball  quite  hot  in  a 
flame,  and  ascertain  by  trying  to  pass  it  through  the 
ring  whether  it  has  increased  in  size.  Devise  some 
method  of  passing  it  through  the  ring  without  cooling 
the  ball. 

Experiment  92.  —  Figure  122  represents  a  thin 
lal'  brass  plate  and  an  iron  plate  of  the  same  dimensions 
riveted  together  so  far  as  to  form  what  is  called  a  compound  bar. 
Place  the  bar  edgewise  in  a  flame,  dividing  the  flame  in  halves  (one- 


EFFECTS  OF   HEAT.  —  EXPANSION.  131 

half  on  each  side  of  the  bar)  so  that  both  metals  may  be  equally 
heated.  The  bar,  which  was  at  first  straight,  is  now  bent,  owing  to 
the  unequal  expansion  of  the  two  metals  on  receiving  equal 
increments  of  heat.  Which  metal  expands  more  rapidly? 
Thrust  the  hot  bar  into  cold  water.  What  happens  ?  Cover 
the  bar  with  chips  of  ice.  What  happens? 

Experiment  93.  —  Fit  stoppers  (perforated  rubber  stop- 
pers are  best)  tightly  in  the  necks  of  two  similar  thin 
glass  flasks  (or  test-tubes),  and  through  each  stopper  pass 
a  glass  tube  about  18  inches  long.  The  flasks  should  be 
nearly  of  the  same  size.  Fill  one  flask  with  water  and  the 
other  with  alcohol,  and  crowd  in  the  stoppers  so  as  to  force 
the  liquids  up  the  tubes  a  little  way  above  the  stoppers. 
Set  both  flasks  at  the  same  time  into  a  large  basin  of  hot 
water  in  order  that  both  may  have  the  same  opportunity  to 
acquire  heat.  Soon  the  liquids  begin  to  expand  and  rise  in  the 
tubes.  Which  liquid  is  more  expansible  ? 

Experiment  94.  — Take  a  dry  flask  like  that  used  in  Experiment 
94,  insert  the  end  of  the  tube  in  a  bottle  of 
colored  water  (Fig.  123),  and  apply  heat  to  the 
flask ;  the  enclosed  air  expands  and  comes  out 
through  the  liquid  in  bubbles.  After  a  few 
minutes,  withdraw  the  heat,  keeping  the  end 
of  the  tube  in  the  liquid ;  as  the  air  left  in  the 
flask  cools,  it  loses  some  of  its  tension,  and 
the  water  is  forced  by  atmospheric  pressure  up 
the  tube  into  the  flask,  and  partially  fills  it. 

Experiment  95.  —  Partly  fill  a  foot-ball  (see 
Fig.  9,  page  8)  with  cold  air,  close  the  orifice, 
and  place  it  near  a  fire.  The  air  will  expand 
and  distend  the  ball. 

Different  substances,  both  in  the  solid 
and  liquid  states,  expand  unequally  on  Flg'  133< 

experiencing  equal  changes  of  temperature.  Except  at 
very  low  temperatures,  all  gases  expand  alike  for  equal 
changes  of  temperature.  Under  uniform  pressure  (as  is 
very  nearly  the  case  in  the  experiment  with  the  balloon) 


132  MOLECULAR   ENERGY.  —  HEAT. 

the  volume  of  any  body  of  gas  varies  -^  its  volume  at 
the  freezing-point  of  water  for  every  degree  Centigrade, 
or  l  for  every  degree  Fahrenheit,  its  temperature  is 
changed.  But  if  the  gas  is  confined  in  a  vessel  of  rigid 
sides,  so  that  its  volume  is  necessarily  constant,  then 
its  tension  varies  in  the  same  ratio  for  every  degree  its 
temperature  is  changed. 

The. force  exerted  by  bodies  in  expanding  or  contracting  is  very  great, 
as  shown  by  the  following  rough  calculation :  If  an  iron  bar,  1  square  inch 
in  section,  is  raised  from  0°  C.  (freezing-point  of  water)  to  500°  C.  (a  dull, 
red  heat),  its  length,  if  allowed  to  expand  freely,  will  be  increased  from 
1  to  1.006.  Now,  a  force  capable  of  stretching  a  bar  of  iron  of  1  square 
inch  section  this  amount  is  about  90  tons,  which  represents  very  nearly  the 
force  that  would  be  necessary  to  prevent  the  expansion  caused  by  heat. 
It  would  require  an  equal  force  to  prevent  the  same  amount  of  contraction 
if  the  bar  is  cooled  from  500°  to  0°  C. 

Boiler  plates  are  riveted  with  red-hot  rivets,  which,  on  cooling,  draw  the 
plates  together  so  as  to  form  very  tight  joints.  Tires  are  fitted  on  carriage- 
wheels  when  red  hot,  and,  on  cooling,  grip  them  with  very  great  force. 

1O6.  Abnormal  Expansion  and  Contraction  of  Water. 

—  Water  presents  a  partial  exception  to  the  general  rule 
that  matter  expands  on  receiving  heat  and  contracts  on 
losing  it.  If  a  quantity  of  water  at  0°  C.,  or  32°  F.,  is 
heated,  it  contracts  as  its  temperature  rises,  until  it  reaches 
4°  C.,  or  about  39°  F.,  when  its  volume  is  least,  and  there- 
fore it  has  its  maximum  density.  If  heated  beyond  this 
temperature,  it  expands,  and  at  about  8°  C.  its  volume  is 
the  same  as  at  0°.  On  cooling,  water  reaches  its  maximum 
density  at  4°  C.,  and  expands  as  the  temperature  falls  be- 
low that  point. 


THERMOMETRY.  133 

Section  IV. 

THERMOMETRY. 

A  thermometer  primarily  indicates  changes  in  volume ; 
but  as  changes  of  volume  are  caused  by  changes  of  tem- 
perature, it  is  commonly  used  for  the  more  important  pur- 
pose of  indicating  temperature. 

107.  Construction  of  a  Thermometer.  —  A  thermom- 
eter generally  consists  of  a  glass  tube  of  capillary  bore, 
terminating  at  one  end  in  a  bulb.     The  bulb  and  part  of 
the  tube  are  filled  with  mercury,  and  the  space  in  the  tube 
above  the  mercury  is  usually  a  vacuum.     On  the  tube,  or 
on  a  plate  behind  the  tube,  is  a  scale  to  show  the  hight  of 
the  mercurial  column. 

108.  Standard  Temperatures.  —  That  a  thermometer 
may  indicate  any  definite  temperature,  it  is  necessary  that 
its  scale  should  relate  to  some  definite  and  unchangeable 
points  of  temperature.     Fortunately  nature  furnishes  us 
with  two  convenient  standards.     It  is  found  that  under 
ordinary  atmospheric  pressure  ice   always   melts   at   the 
same  temperature,  called  the  melting-point,  or,  more  com- 
monly, the  freezing-point  (water  freezes  and  ice  melts  at 
the  same  temperature).     Again,  the  temperature  of  steam 
rising  from  boiling  water  under  the  same  pressure  is  always 
the  same. 

109.  Graduation  of  Thermometers.  —  The  bulb  of  a 
thermometer  is  first  placed  in  melting  ice  (Fig.  124),  and 
allowed  to  stand  until  the  surface  of  the  mercury  becomes 


134 


MOLECULAR  ENERGY.  —  HEAT. 


stationary,  and  a  mark  is  made  upon  the  stem  at  that 
point,  and  indicates  the  freezing-point.  Then  the  instru- 
ment is  suspended  in  steam  rising  from  boiling  water  (Fig. 
125),  so  that  all  but  the  very  top  of  the  column  is  in  the 
steam.  The  mercury  rises  in  the  stem  until  its  tempera- 
ture becomes  the  same  as  that  of  the  steam,  when  it  again 
becomes  stationary,  and  another  mark  is  placed  upon  the 
stem  to  indicate  the  boiling-point.  Then  the  space  be- 


Fig.  124. 


Fig.  135. 


tween  the  two  points  found  is  divided  into  a  convenient 
number  of  equal  parts  called  degrees,  and  the  scale  is  ex- 
tended above  and  below  these  points  as  far  as  desirable. 

Two  methods  of  division  are  adopted  in  this  country: 
by  one,  this  space  is  divided  into  180  equal  parts,  and  the 
result  is  called  the  Fahrenheit  scale,  from  the  name  of  its 
author ;  by  the  other,  the  space  is  divided  into  100  equal 
parts,  and  the  resulting  scale  is  called  centigrade,  which 
means  one  hundred  steps.  In  the  Fahrenheit  scale,  which 
is  generally  employed  in  English-speaking  countries  for 
ordinary  household  purposes,  the  freezing  and  boiling 


THEKMOMETKY. 


135 


points  are  marked  respectively  32°  and  212°. 
The  0  of  this  scale  (32°  below  freezing- 
point),  which  is  about  the  lowest  tempera- 
ture that  can  be  obtained  by  a  mixture  of 
snow  and  salt,  was  incorrectly  supposed  to 
be  the  lowest  temperature  attainable.  The 
centigrade  scale,  which  is  generally  em- 
ployed by  scientists,  has  its  freezing  and 
boiling  points  more  conveniently  marked, 
respectively  0°  and  100°.  A  temperature  be- 
low 0°  in  either  scale  is  indicated  by  a  minus 
sign  before  the  number.  Thus,  — 12°  F.  in- 
dicates 12°  below  0°  (or  44°  below  freezing- 
point),  according  to  the  Fahrenheit  scale. 

To  reduce  a  Fahrenheit  reading  to  a 
centigrade  reading,  first  subtract  32  from 
the  given  number,  and  then  multiply  by  f . 

Thus, 

|(F-32)=C. 

To  change  a  centigrade  reading  to  a  Fah- 
renheit reading,  first  multiply  the  given 
number  by  -§-,  and  then  add  32.  Thus, 

f  C  +  32  =  F. 


toir 


32* 


Fig.  126. 


EXERCISES. 

1.  Express  the  following  temperatures  of  the  centigrade  scale  in  the 
Fahrenheit  scale:  100°;  40°;  56°;  60°;  0°;  -20°;  -40°;  80°;  150. 

NOTE.  —  In  adding  or  subtracting  32°,  it  should  be  done  algebraically. 
Thus,  to  change  —  14°  C.  to  its  equivalent  on  the  Fahrenheit  scale :  f  X 
(_  14)  =  _  25.2°  ;  —25.2° +  32°  =6.8°,  the  required  temperature  on  the 
Fahrenheit  scale.  Again,  to  find  the  equivalent  of  24°  F.  in  the  centi- 
grade scale  :  24  —  32  =  —  8;  —  8  X  f  =  —  4| ;  hence,  24°  F.  is  equivalent 
to  -  4.4°  +  C. 

2.  Express  the  following  temperatures  of  the  Fahrenheit  scale  in  the 
centigrade  scale  :  212°  ;  32°  ;  90°  ;  77°  ;  20° ;  10° ;  -  10° ;  -  20° ;  -40° ; 
40°  ;  59° ;  329°. 


136  MOLECULAR   ENEKGY. — HEAT. 


Section  V. 

EFFECTS  OF  HEAT  CONTINUED. — LIQUEFACTION   AND 
VAPORIZATION. 

11O.  Liquefaction.  —  As  previously  stated  (page  9), 
whether  a  body  exist  in  a  solid,  liquid,  or  gaseous  state 
depends  upon  its  temperature  and  the  pressure  which  it  is 
under. 

Experiment  96.  —  Take  a  lump  of  ice  as  large  as  your  two  fists, 
put  it  into  boiling  water ;  when  reduced  to  about  \  its  original  size 
skim  it  out.  Wipe  the  lump,  and  place  one  hand  on  it  and  the  other 
on  a  lump  to  which  heat  has  not  been  applied.  Do  you  perceive  any 
difference  in  their  temperatures?  Ice  reduces  the  temperature  of 
victuals  in  our  refrigerators ;  do  the  victuals  raise  the  temperature  of 
the  ice?  How  does  the  heat  which  the  victuals  impart  to  the  ice 
affect  it? 

Experiments  and  experience  teach  that  (1)  the  melting 
or  solidifying  point  (they  are  always  the  same  for  the  same 
substance)  may  vary  widely  for  different  substances,  but 
for  the  same  substance  it  is  invariable  when  under  the  same 
pressure. 

(2)  The  temperature  of  a  solid  or  liquid  remains  con- 
stant at  the  melting-point  from  the  moment  that  melting  or 
solidification  begins. 

111.    Vaporization. 

Experiment   97.  —  Place   a  test-tube    (Fig.   127), 
'naif  filled  with  ether,  in  a  beaker  containing  water  at 
a  temperature  of  60°  C.     Although  the  temperature  of 
the  water  is  40°  below  its  boiling-point,  it  very  quickly 
raises  the  temperature  of  the  ether  sufficiently  to  cause 
Fig.  137.       it  to  boil  violently.    Introduce  a  chemical  thermometer1 
into  the  test-tube,  and  ascertain  the  boiling-point  of  ether. 

1  A  chemical  thermometer  has  its  scale  on  the  glass  stem,  instead  of  a  plate,  and  is 
otherwise  adapted  to  experimental  use. 


LIQUEFACTION   AND   VAPORIZATION. 


137 


Experiment  98.  —  Take  two  beakers  half  full  of  water.  Raise 
both  to  the  boiling-point.  Dissolve  pulverized  saltpetre  in  one  as 
long  as  it  readily  dissolves.  Suspend  in  both  liquids  chemical  ther- 
mometers, so  that  the  bulb  of  each  shall  be  within  one  inch  of  the 
bottom.  Does  the  boiling  water,  as  you  continue  to  apply  heat,  get 
hotter?  Is  the  boiling  solution  any  hotter  than  the  boiling  water? 
Does  the  solution  get  hotter  as  it  becomes  concentrated  by  loss  of 
water  by  vaporization  ? 

After  a  liquid  begins  to  boil,  the  temperature  remains  con- 
stant until  the  whole  is  vaporized,  if  the  density  of  the  liquid 
and  the  pressure  remain  constant. 

Experiment  99.  — Place  a  beaker,  half  full  of  water  at  80°  C., 
under  the  receiver  of  an  air-pump,  and  exhaust  the  air.  The  water, 
though  far  below  its  usual  boiling-point,  boils  violently.  Readmit  the 
air,  and  test  the  temperature  of  the  water  which  has  just  been  boiling. 


Fig.  128. 


Fig.  129. 


Experiment  100.  —  Half  fill  a  thin  glass  flask  with  water.  Boil 
the  water  over  a  Bunsen  burner;  the  steam  will  drive  the  air  from 
the  flask.  Withdraw  the  burner,  quickly  cork  the  flask  very  tightly, 
invert  the  flask,  and  pour  cold  water  upon  the  part  containing  steam, 
as  in  Figure  128 ;  the  water  in  the  flask,  though  cooled  several  degrees 


138 


MOLECULAK  ENERGY.  —  HEAT. 


below  the  usual  boiling-point,  boils  again  violently.  The  application 
of  cold  water  to  the  flask  condenses  some  of  the  steam,  and  diminishes 
the  tension  of  the  rest,  so  that  the  pressure  upon  the  water  is  dimin- 
ished, and  the  water  boils  at  a  reduced  temperature. 

If  hot  water  is  poured  upon  the  flask,  the  water  ceases  to  boil. 
Why? 

Experiment  101.  —  Provide  a  tumbler  of  cold  water,  a  test-tube 
nearly  filled  with  water,  tightly  stoppered,  and  having  glass  tubes  ex- 
tending through  the  stopper,  as  represented  in  Figure  129.  Place  the 
exposed  end  of  the  bent  tube  in  the  tumbler  of  water,  and  apply  heat  to 
the  bottom  of  the  test-tube,  and  boil  the  water  for  about  five  minutes. 
Then  remove  the  heat,  leave  the  end  of  the  tube  in  the  tumbler  of 
water,  and  allow  the  water  of  the  test-tube  to  cool  for  some  time ;  or, 

better,  to  hasten  the 
cooling,  place  the  test- 
tube  in  another  tum- 
bler of  cold  water.  Ob- 
serve carefully,  and 
explain  all  phenomena 
which  occur  from  the 
beginning  to  the  end 
of  the  operation. 


112.  Distillation. 

Experiment  102.  — 
Vessel  A  (Fig.  130) 
(called  a  condenser) 
contains*a  coil  (called* 
a  worm)  of  copper 
tube,  terminating  at 


Fig.  130. 

one  extremity  at  a.  The  other  end  of  the  tube,  &,  projects  through 
the  side  of  the  vessel  near  its  bottom.  Near  the  top  of  the  vessel 
projects  another  tube,  c  (called  the  overflow),  with  which  is  con- 
nected a  rubber  tube,  e.  This  tube  conveys  the  warm  water  which 
rises  from  the  surface  of  the  heated  worm  away  to  a  sink  or  other 
convenient  receptacle. 

Take  a  glass  flask  of  a  quart  capacity,  fill  it  three-fourths  full  of  pond 
or  bog  water.  Connect  the  flask  by  means  of  a  glass  delivery-tube  with 
the  extremity  a  of  the  worm.  Heat  the  water  in  the  flask ;  as  soon  as 


LIQUEFACTION  AND   VAPORIZATION.  139 

it  begins  to  boil,  commence  siphoning  cold  water  through  a  small  tube, 
d,  from  an  elevated  vessel  E  into  the  condenser.  Inasmuch  as  the  worm 
is  constantly  surrounded  with  cold  water,  the  steam  on  passing  through 
it  becomes  condensed  into  a  liquid,  and  the  liquid  (called  the  distillate} 
trickles  from  the  extremity  b  into  a  receiving  vessel.  The  distillate 
is  clear,  but  the  water  in  the  flask  acquires  a  yellowish  brown  tinge 
as  the  boiling  progresses,  due  to  the  concentration  of  impurities 
(largely  of  vegetable  matter)  which  are  held  in  suspension  and  solu- 
tion in  ordinary  pond  water.  The  apparatus  used  is  called  a  still,  and 
the  operation  distillation. 

When  a  volatile  liquid  is  to  be  separated  from  water,  for  example, 
when  alcohol  is  separated  from  the  vinous  mash  after  fermentation  (see 
Chemistry,  page  184),  the  mixed  liquid  is  heated  to  its  boiling-point,  which 
is  lower  than  that  of  water.  Much  more  of  the  volatile  liquid  will  be  con- 
verted into  vapor  than  of  the  water,  because  its  boiling  point  is  lower. 
Thus  a  partial  separation  is  effected.  By  repeated  distillations  of  the 
distillate,  a  95  per  cent  alcohol  is  obtained. 

113.  Evaporation.  —  In  boiling,  the  heat,  applied  at 
the  bottom,  rapidly  converts  the  liquid  into  vapor,  which, 
rising  in  bubbles  and  breaking  at  or  near  the  surface,  pro- 
duces a  violent  agitation  in  the  liquid,  called  boiling  or 
ebullition.  Boiling  takes  place  only  at  a  definite  tempera- 
ture, which  depends  on  the  kind  of  liquid  and  the  pressure 
that  is  on  it.  Evaporation  is  that  form  of  vaporization 
which  takes  place  quietly  and  slowly  at  the  surface.  Al- 
though hastened  by  heat,  the  evaporation  of  water  occurs 
at  any  temperature,  however  low;  even  ice  and  snow 
evaporate. 

The  rapidity  of  evaporation  increases  with  the  tempera- 
ture, amount  of  surface  exposed,  dry  ness  of  the  atmosphere, 
and  diminution  of  pressure.  This  vapor  of  water  mixes 
freely  with  the  air,  and  diffuses  rapidly  through  it,  acting 
like  another  gas.  A  given  space,  —  for  example,  a  cubic 
foot  (it  matters  little  whether  there  is  air  in  the  space  or 
whether  it  is  a  vacuum),  can  hold  only  a  limited  amount 


140  MOLECULAR  ENERGY.  —  HEAT. 

of  water  vapor.  This  quantity  depends  on  the  tempera- 
ture of  the  vapor.  The  capacity  of  a  space  for  water 
vapor  increases  rapidly  with  the  temperature,  being  nearly 
doubled  by  a  rise  of  10°  C.  When  a  space  contains  such 
an  amount  of  water  vapor  that  its  temperature  cannot  be 
lowered  without  some  of  the  water  being  precipitated  in 
the  form  of  a  liquid,  the  vapor  is  said  to  be  saturated, 
and  the  temperature  at  which  this  happens  is  called  the 
dew-point. 

Experiment  103.  —  Take  a  bright  nickel-plated  cup,  such,  for  ex- 
ample, as  are  used  for  lemonade-shakers ;  pour  into  it  a  small  quantity 
of  tepid  water.  Place  in  the  water  the  bulb  of  a  chemical  thermome- 
ter. Gradually  reduce  the  temperature  of  the  water  by  stirring  into 
it  ice  water  until  you  discover  a  slight  dimness  of  the  luster  of  that 
portion  of  the  outside  of  the  cup  next  the  water.  If  the  ice  water 
does  not  reduce  the  temperature  sufficiently,  add  ice,  keeping  the  mix- 
ture briskly  stirring.  If  the  ice  does  not  answer,  pour  out  some  of 
the  water  and  sprinkle  salt  on  the  ice,  keeping  the  bulb  of  the  ther- 
mometer in  the  remaining  water.  Note  the  temperature  of  the  water 
at  the  instant  that  the  first  mist  or  dimness  appears  on  the  cup. 
Wait  until  the  dimness  or  mist  disappears,  and  note  the  temperature 
of  the  water  when  the  last  disappears.  Take  the  mean  of  the  two 
temperatures  for  the  dew-point. 

The  form  in  which  the  condensed  vapor  appears  is,  according  to  its 
location,  dew,  fog,  or  cloud.1  The  atmosphere  is  said  to  be  dry  or  humid, 
not  according  to  the  quantity  of  water  vapor  which  it  at  any  time  contains, 
but  according  as  it  can  contain  much  or  little  more  than  it  has.  The  air 
in  summer  months  usually  contains  a  large  amount  of  water  vapor,  yet  it 
is  usually  very  dry.  The  heat  of  a  stove  dries  the  air  of  a  room  without 
destroying  any  of  its  water  vapor.  In  such  a  room,  the  lips,  tongue, 
throat,  and  skin  experience  a  disagreeable  sensation  of  dryness,  owing  to 
the  rapid  evaporation  which  takes  place  from  their  surfaces.  This  should 
be  taken  as  nature's  admonition  to  keep  water  in  the  stove  urns,  and 
tanks  connected  with  furnaces. 

1  A  cloud  is  simply  a  fog  in  an  elevated  region  of  the  atmosphere.  It  is  composed  of 
minute  spheres  of  water  from  jfa,  to  T!&u  of  an  inch  in  diameter. 


HEAT   CONVERTIBLE  INTO   POTENTIAL  ENERGY.       141 


Section  VI. 

HEAT  CONVERTIBLE  INTO   POTENTIAL   ENERGY,  AND  VICE 

VERSA. 

114.  Heat  Units.  —  It  is  frequently  necessary  to  meas- 
ure quantity  of  heat,  and  for  this  purpose  a  standard  unit 
of  measurement  is  required.  The  heat  unit  generally 
adopted  is  the  amount  of  heat  required  to  raise  the  tempera- 
ture of  one  kilogram  of  water  from  0°  to  1°  C.  This  unit  is 
called  a  calorie. 

Let  it  be  required  to  find  approximately  the  amount  of 
heat  that  disappears  during  the  melting  of  one  kilogram 
of  ice. 

Experiment  104.  —  Weigh  out  200^  of  dry  (dry  it  with  a  towel) 
ice  chips  whose  temperature  in  a  room  of  ordinary  temperature  may 
be  safely  assumed  to  be  0°  C.  Weigh  out  200^  of  boiling  water,  whose 
temperature  we  assume  to  be  100°  C.  Pour  the  hot  water  upon  the 
ice,  and  stir  until  the  ice  is  all  melted.  Test  the  temperature  of  the 
resulting  liquid. 

Suppose  its  temperature  is  found  to  be  10°  C.  It  is  evident  that 
the  temperature  of  the  hot  water  in  falling  from  100°  to  90°  would 
yield  sufficient  heat  to  raise  an  equal  weight  of  water  from  0°  to  10° 
C.  Hence  it  is  clear  that  the  heat  which  the  water  at  90°  yields  in 
falling  from  90°  to  10°  —  a  fall  of  80°  —  in  some  manner  disappears. 
At  this  rate  had  you  used  lk  of  ice  and  lk  of  hot  water,  the  amount  of 
heat  lost  would  be  80  calories.  Careful  experiments,  in  which  suit- 
able allowances  are  made  for  loss  or  gain  of  heat  by  radiation  and 
conduction,  have  determined  that  80  calories  of  heat  are  consumed  in 
melting  1  kilogram  of  ice.  How  near  to  this  do  the  results  of  your  ex- 
periments approach  ? 

Next  let  it  be  required  to  find  the  amount  of  heat  that  disappears 
during  the  conversion  of  1  kilogram  of  water  into  steam . 

Experiment  105.  —  Take  in  a  porcelain  evaporating-dish  50s  of 


142          MOLECULAR  ENERGY.  —  HEAT. 

ice  water  at  (say)  5°  C.  Place  it  over  a  flame,  and,  watch  in  hand, 
note  the  time  in  seconds  which  elapses  before  it  boils.  Then  note 
the  time  which  elapses  before  it  is  all  converted  into  steam.  Suppose 
that  it  required  100  seconds  to  raise  the  water  from  5°  to  its  boiling- 
point,  which  we  assume  is  100°  —  a  rise  of  95° ;  and  that  it  requires 
530  seconds  to  convert  the  water,  after  it  commences  to  boil,  into 
steam.  Then  the  latter  operation  consumes  (  530 -f- 100=)  about  5.3 
times  as  much  time  as  the  former.  But  the  heat  applied  to  the  water 
while  boiling  does  not  raise  its  temperature  (see  Exp.  98,  page  137)  ; 
then  all  the  heat  given  to  the  water  during  the  interval  of  time  dis- 
appears. Had  you  taken  lk  of  water,  it  would  have  required  95  calo- 
ries to  raise  the  water  from  5°  to  100°  C.  Hence,  in  converting  the 
lk  of  water  into  steam,  95x5.3=  (about)  503  calories  disappear. 
Accurate  methods  have  determined  that  537  calories  disappear  during 
the  conversion  of  lk  of  water  into  steam. 

The  heat  which  disappears  in  melting  and  boiling  is 
generally,  but  with  our  present  knowledge  of  the  subject, 
rather  objectionably,  called  latent  (hidden)  heat.  The 
error  consists  in  calling  that  heat  which  has  ceased  to  be 
heat.  The  heat,  i.e.  kinetic  energy,  that  disappears  in 
melting  is  consumed  in  doing  interior  (i.e.  molecular)  work. 
The  molecules  that  in  the  solid  are  held  firmly  in  their 
places  by  molecular  forces,  are  moved  from  their  places 
during  melting,  and  so  work  is  done  against  these  forces, 
much  as  work  is  done  against  gravity  when  a  stone  is 
raised.  In  both  cases  kinetic  energy  is  consumed — disap- 
pears; but  this  means  simply  that  it  is  transformed  into 
potential  energy.  The  so-called  latent  heat  is  simply  a 
misnomer  for  molecular  potential  energy. 

When  water  is  converted  into  steam,  the  larger  portion  of  the  heat, 
which  is  rendered  latent,  is  consumed  in  separating  the  molecules  so  far 
that  molecular  attraction  is  no  longer  sensible ;  a  small  portion  —  about 
Jg — is  consumed  in  overcoming  atmospheric  pressure.  The  amount  of 
work  done  in  melting  and  boiling  —  especially  the  latter  —  is  very  great, 
as  shown  by  the  amount  of  heat  consumed.  Hence  it  requires  a  long  time 
to  acquire  the  requisite  amount  of  heat.  This  is  a  protection  against 


HEAT   CONVERTIBLE  INTO  POTENTIAL   ENERGY.      143 

sudden  changes.  For  example,  if  snow  and  ice  melted  immediately  on 
reaching  the  melting-point,  all  the  snow  and  ice  would  melt  in  a  single 
warm  day  in  winter,  creating  most  destructive  freshets. 

115.  Potential  Energy  converted  into  Heat  by  the 
Solidification  of  Liquids  and  the  Liquefaction  of 
Vapors.  —  If  our  theory  be  true  that  heat  is  converted 
into  potential  energy  during  vaporization  and  melting, 
then  ought  the  energy  to  be  restored  to  the  kinetic  state 
(i.e.  the  heat  which  disappears  during  these  operations 
ought  to  be  restored)  when  the  molecules  return  to  their 
original  positions,  i.e.  when  vapor  becomes  liquid,  or  when 
liquids  solidify. 

Experiment  106.  — Take  in  a  beaker  C  (Fig.  131)  lk  of  water  at 
(say)  12°  C.  Take  about 
500«  of  water  in  a  flask  A, 
and  raise  it  to  the  boiling- 
point.  As  soon  as  it  be- 
gins to  boil,  connect  the 
flask  with  the  beaker  by 
a  delivery-tube  B,  carry- 
ing the  end  of  the  tube 
nearly  to  the  bottom  of  the 
beaker.  When  about  one- 
fifth  of  the  water  has  boiled 
away,  remove  the  delivery 
tube  from  C,  and  immedi-  Fig<  131' 

ately  test  the  temperature  of  the  water  in  the  beaker,  and  weigh  it. 
Assume  that  the  temperature  of  the  steam  is  100°  C.,  and  we  will 
suppose,  for  illustration,  that  there  are  1,100"  of  water  now  in  the 
beaker;  then  100s  of  water  have  been  converted  into  steam  which 
has  passed  into  the  beaker  and  been  condensed  or  liquefied  by  the 
cold  water.  Suppose,  again,  that  the  temperature  of  the  water 
in  the  beaker  was  raised  thereby  to  70°  C.  Now  1008  of  water  at 
100°  C.  (resulting  from  the  condensation  of  the  steam)  in  falling  to 
70°  C.  could  yield  (30-r-10=)  only  3  calories;  hence  it  could  raise  the 
lk  of  water  only  3°;  i.e.  from  12°  to  15°  C.  Then  it  is  evident  that 
it  must  have  acquired  the  balance  of  (70  — 15  =)  55  calories,  by  the 


144  MOLECULAR   ENEEGY. — HEAT. 

restoration  of  the  latent  heat  to  real  heat  when  the  steam  is  liquefied. 
If  the  liquefaction  of  100s  of  steam  yields  55  calories,  then  the  lique- 
faction of  lk  of  steam  would  yield  550  calories.  Accurate  methods 
give  537  calories. 

Various  phenomena  show  that  heat  is  developed  during  the  solidifica- 
tion of  liquids,  but  as  the  development  is  slow,  and  the  loss  by  radiation 
rapid,  it  is  difficult  to  make  measurements.  There  are  good  reasons  for 
assuming,  however,  that  there  are  80  calories  of  heat  generated  for  every 
kilogram  of  water  that  is  frozen.  Farmers  sometimes  turn  to  practical 
use  this  well-known  phenomenon.  Anticipating  a  cold  night,  they  carry 
tubs  of  water  into  cellars  to  be  frozen.  The  heat  generated  thereby, 
although  of  a  low  temperature,  is  sufficient  to  protect  vegetables  which 
freeze  at  a  lower  temperature  than  water. 

Steam  is  a  most  convenient  vehicle  for  the  conveyance  of  latent  heat. 
For  example,  every  kilogram  of  steam  that  is  condensed  in  the  radiator 
box  (Fig.  120,  p.  128)  contributes  to  the  air  which  passes  through  the  box 
537  calories,  or  heat  sufficient  to  raise  5.37k  of  ice  water  to  the  boiling- 
point. 

116.  Methods    of   Producing  Artificial   Cold.  — The 

fact  that  heat  must  be  consumed  because  work  is  done,  in 
the  conversion  of  solids  into  liquids  and  liquids  into 
vapors,  is  turned  to  practical  use  in  many  ways  for  the 
purpose  of  producing  artificial  cold.  The  following  ex- 
periments will  illustrate. 

117.  Cold  by  Dissolving.  —  Freezing  Mixtures. 

Experiment  107.  —  Prepare  a  mixture  of  2  parts,  by  weight,  of 
pulverized  ammonium  nitrate  and  1  part  of  ammonium  chloride. 
Take  about  75CC  of  water  (not  warmer  than  8°  C.),  and  into  it  pour 
a  large  quantity  of  the  mixture,  stirring  the  same,  while  dissolving, 
with  a  test-tube  containing  a  little  cold  water.  The  water  in  the 
test-tube  will  be  quickly  frozen.  A  finger  placed  in  the  solution  will 
feel  a  painful  sensation  of  cold,  and  a  thermometer  will  indicate  a 
temperature  of  about  — 10°  C. 

One  of  the  most  common  freezing  mixtures  consists  of 
3  parts  of  snow  or  broken  ice  and  1  part  of  common  salt. 
The  affinity  of  salt  for  water  causes  a  liquefaction  of  the 


HEAT   CONVERTIBLE  INTO  POTENTIAL  ENERGY.     145 

ice,  and  the  resulting  liquid  dissolves  the  salt,  both  opera- 
tions requiring  heat. 

118.     Cold  by  Evaporation. 

Experiment  108.  —  Fill  the  palm  of  the  hand  with  ether;  the 
ether  quickly  evaporates,  and  produces  a  painful  sensation  of  cold. 

Experiment  109. —  Place  water  at  about  30°  C.  in  a  thin  porous 
cup,  such  as  is  used  in  the  Grove's  battery,  and  the  same  amount  of 
water,  at  the  same  temperature,  in  a  glass  beaker  of  as  nearly  as  pos- 
sible the  same  size  as  the  porous  cup.  Introduce  into  each  a  chemi- 
cal thermometer.  The  comparatively  large  amount  of  surface  exposed 
by  means  of  the  porous  vessel  will  so  hasten  the  evaporation  in  this 
vessel,  that,  in  the  course  of  10  to  15 
minutes,  quite  a  sensible  difference  of 
temperature  will  be  indicated  by  the 
thermometers  in  the  two  vessels. 

Experiment  110.  —  Cover  closely  the 
bulb  of  an  air  thermometer  (Fig.  132) 
with  thin  muslin,  and  partly  fill  the  stem 
with  water.  Let  one  person  slowly  drop 
ether  on  the  bulb,  while  another  briskly 
blows  the  air  charged  with  vapor  away 
from  the  bulb  with  a  bellows ;  or,  place 
the  bulb  in  a  window  whose  sash  is  raised 
a  little  way,  so  as  to  be  in  a  draft.  As 

the  air  changes  rapidly,  it  does  not  become  saturated  with  vapor  so 
as  to  impede  evaporation,  and  in  10  to  15  minutes  the  water  in  the 
stern  freezes,  even  in  a  warm  room. 

The  evaporation  of  perspiration  conduces  to  our  health  and  comfort  by 
relieving  us  of  surplus  heat.  We  cool  the  fevered  forehead  by  bathing  it 
with  a  volatile  liquid,  such  as  a  solution  of  alcohol  in  water.  Windy  days 
seem  colder  to  us  than  still  days,  although  the  temperature  of  both  is  the 
same,  because  evaporation  of  perspiration  takes  place  more  rapidly  in  a 
changing  air.  Fanning  in  a  similar  way  changes  the  air  next  our  persons, 
thereby  quickening  the  evaporation  of  the  perspiration,  and  cooling  the 
surface  of  the  body.  Ice  is  now  manufactured  in  large  quantities  during 
the  summer  season  in  warm  climates  by  the  evaporation  of  liquid  ammo- 
nia. Evaporation  is  the  most  efficient  means  of  producing  extremely 
low  temperatures. 


146  MOLECULAR  ENERGY.  —  HEAT. 

QUESTIONS. 

1.  How  can  water  be  made  to  boil  at  a  low  temperature  ? 

2.  Upon  what  does  the  tension  of  steam  depend  ? 
2.  Why  can  you  not  make  ice  warm  ? 

4.  Does  ice  always  have  the  same  temperature ;  i.e.  can  it  be  made 
colder  than  32°  F.  ? 

5.  What  is  the  lowest  temperature  any  body  can  have  ? 

6.  (a)  Where  does  the  "  sweat "  on  ice-pitchers  come  from  ?  (&)  Where 
does  dew  on  grass  come  from  ?    (c)  How  are  clouds  formed  ? 

7.  (a)  When   the   sweat  on   ice-pitchers  is  very  abundant,  what 
does  it  indicate  about  dew-point  ?    (&)  Does  it  forebode  fair  or  rainy 
weather  ? 

8.  How  will  you  easily  show  that  ether  boils  at  a  lower  tempera- 
ture than  water  ? 

9.  In  which  will  vegetables  cook  quicker,  —  in  fresh  or  salt  water  ? 

10.  How  could  you  separate  the  alcohol  of  rum  or  brandy  from 
the  watery  part  ? 

11.  (a)  On  what  kind  of  days  do  clothes  dry  fastest?    (b)  Will 
frozen  clothes  dry  ? 

12.  (a)  How  does  heat  dry  the  air?    (b)  How  does  heat  dry  clothes  ? 

13.  Suppose  that  10k  of  steam,  at  100°  C.,  is  condensed  in  the 
steam-pipe  in  the  radiator  box,  Figure  120,  per  hour ;  how  much  heat 
will  it  furnish  to  the  surrounding  air  ? 

14.  How  much  heat  will  be  produced  by  freezing  one  cubic  foot 
(about  29k)  62.5  pounds  of  water? 


THERMO-DYNAMICS.  147 

Section  VII. 

THERMO-DYNAMICS. 

119.  Thermo-dynamics  Defined.  —  Thermo-dynamics  is 
that  branch  of  science  that  treats  of  the  relation  between  heat 
and  mechanical  work.     One  of  the  most  important  discov- 
eries in  science  is  that  of  the  equivalence  of  heat  and  work; 
that  is,  that  a  definite  quantity  of  mechanical  work,  when 
transformed  without  waste,  will  yield  a  definite  quantity  of 
heat;  and  conversely,  this  heat,  if  there  were  no  waste,  could 
perform  the  original  quantity  of  mechanical  work. 

120.  Transformation,  Correlation,  and  Conservation 
of  Energy.  —  The  proof  of  the  facts  just  stated  was  one  of 
the  most  important  steps  in  the  establishment  of  the  grand 
twin  conceptions  of  modern  science  :    (1)  That  all  kinds  of 
energy  are  so  related  to  one  another  that  energy  of  any  kind 
can  be  transformed  into  energy  of  any  other  kind,  —  known 
as  the  doctrine  of  CORRELATION  OF  ENERGY  ;  (2)  That 
when  one  form  of  energy  disappears,  an  exact  equivalent  of 
another  form  ahvays  takes  its  place,  so  that  the  sum  total  of 
energy  is  unchanged,  —  known  as  the  doctrine  of  CONSER- 
VATION OF  ENERGY.     These  two  principles  constitute  the 
corner-stone  of  physical  science.     Chemistry  teaches  that 
there  is  a  conservation  of  matter. 

121.  Joule's  Experiment.  —  The  experiment  to  ascer- 
tain the  "mechanical  value  of  heat,"  as  performed  by  Dr. 
Joule  of  England,  was  conducted  about  as  follows.     He 
caused  a  paddle-wheel  to  revolve  in  water,  by  means  of  a 
falling  weight  attached  to  a  cord  wound  around  the  axle 


148          MOLECULAR  ENERGY.  —  HEAT. 

of  a  wheel.  The  resistance  offered  by  the  water  to  the 
motion  of  the  paddles  was  the  means  by  which  the  mechan- 
ical energy  of  the  weight  was  converted  into  heat,  which 
raised  the  temperature  of  the  water.  Taking  a  body  of  a 
known  weight,  e.g.  80k,  he  raised  it  a  measured  distance, 
e.g.  53m  high;  by  so  doing  4,240kgm  of  work  were  performed 
upon  it,  and  consequently  an  equivalent  amount  of  energy 
was  stored  up  in  it  ready  to  be  converted,  first  into  me- 
chanical motion,  then  into  heat.  He  took  a  definite 
weight  of  water  to  be  agitated,  e.g.  2k,  at  a  temperature  of 
0°  C.  After  the  descent  of  the  weight,  the  water  was 
found  to  have  a  temperature  of  5°  C. ;  consequently  the 
2k  of  water  must  have  received  10  units  of  heat  (careful 
allowance  being  made  for  all  losses  of  heat),  which  is  the 
amount  of  heat-energy  that  is  equivalent  to  4,240kgm  of 
work,  or  one  unit  of  heat  is  equivalent  to  424**"*  of  work. 

122.  Mechanical  Equivalent  of  Heat.  —  As  a  con- 
verse of  the  above  it  may  be  demonstrated  by  actual  ex- 
periment that  the  quantity  of  heat  required  to  raise  1  of 
water  from  0°  to  1°  C.  will,  if  converted  into  work,  raise  a 
424k  weight  lm  high,  or  lk  weight  424m  high.  According 
to  the  English  system,  the  same  fact  is  stated  as  follows : 
The  quantity  of  heat  that  will  raise  1  pound  of  water  1°  F. 
will  raise  772.55  pounds  1  foot  high.  The  quantity,  424kgm, 
is  called  the  mechanical  equivalent  of  one  calorie,  or  Joule's 
equivalent  (abbreviated  simpty  J.).  Or,  we  may  say  that 
one  calorie  is  the  thermal  equivalent  of  424kgm  of  work. 


STEAM-ENGINE.  149 

Section  VIII. 

STEAM-ENGINE. 

123.  Description  of  a  Steam-Engine.  —  A  steam-en- 
gine is  a  machine  in  which  the  elastic  force  of  steam  is  the 
motive  power.  Inasmuch  as  the  elastic  force  of  steam  is 
entirely  due  to  heat,  the  steam-engine  is  properly  a  heat  en- 
gine ;  that  is,  it  is  a  machine  by  means  of  which  heat  is 
continuously  transformed  into  work  or  mechanical  motion. 

The  modern  steam-engine  consists  essentially  of  an  ar- 
rangement by  which  steam  from  a  boiler  is  conducted  to 
both  sides  of  a  piston  alternately ;  and  then,  having  done 
its  work  in  driving  the  piston  to  and  fro,  is  discharged 
from  both  sides  alternately,  either  into  the  air  or  into  a 
condenser.  The  diagram  in  Figure  133  will  serve  to  illus- 
trate the  general  features  and  the  operation  of  a  steam-en- 
gine. The  details  of  the  various  mechanical  contrivances 
are  purposely  omitted,  so  as  to  present  the  engine  as  nearly 
as  possible  in  its  simplicity. 

In  the  diagram,  B  represents  the  boiler,  F  the  furnace, 
S  the  steam-pipe  through  which  steam  passes  from  the 
boiler  to  a  small  chamber  VC,  called  the  valve-chest.  In 
this  chamber  is  a  slide-valve  V,  which,  as  it  is  moved  to 
and  fro,  opens  and  closes  alternately  the  passages  M  and 
N  leading  from  the  valve-chest  to  the  cylinder  C,  and  thus 
admits  the  steam  alternately  each  side  of  the  piston  P. 
When  one  of  these  passages  is  open,  the  other  is  always 
closed.  Though  the  passage  between  the  valve-chest  and 
the  space  in  the  cylinder  on  one  side  of  the  piston  is 
closed,  thereby  preventing  the  entrance  of  steam  into  this 
space,  the  passage  leading  from  the  same  space  is  open 


150 


MOLECULAR  ENERGY.  —  HEAT. 


through  the  interior  of  the  valve,  so  that  steam  can  escape 
from  this  space  through  the  exhaust-pipe  E.  Thus,  in  the 
position  of  the  valve  represented  in  the  diagram,  the  pas- 
sage N  is  open,  and  steam  entering  the  cylinder  at  the  top 
drives  the  piston  in  the  direction  indicated  by  the  arrow. 
At  the  same  time  the  steam  on  the  other  side  of  the  piston 
escapes  through  the  passage  M  and  the  exhaust-pipe  E. 
While  the  piston  moves  to  the  left,  the  valve  moves  to  the 


Fig.  133. 

right,  and  eventually  closes  the  passage  N  leading  from 
the  valve-chest,  opens  the  passage  M  into  the  same,  and 
thus  the  order  of  things  is  reversed. 

Motion  is  communicated  by  the  piston  through  the 
piston-rod  R  to  the  crank  G,  and  by  this  means  the  shaft 
A  is  rotated.  Connected  with  the  shaft  by  means  of  the 


STEAM-ENGINE.  151 

crank  H  is  a  rod  R'  which  connects  with  the  valve  V,  so 
that,  as  the  shaft  rotates,  the  valve  is  made  to  slide  to  and 
fro,  and  always  in  the  opposite  direction  to  that  of  the 
motion  of  the  piston. 

The  shaft  carries  a  fly-wheel  W.  This  is  a  large,  heavy 
wheel,  having  the  larger  portion  of  its  weight  located  near 
its  circumference;  it  serves  as  a  reservoir  of  energy  which 
is  needed  to  make  the  rotation  of  the  shaft  and  all  other 
machinery  connected  with  it  uniform,  so  that  sudden 
changes  of  velocity  resulting  from  sudden  changes  of  the 
driving  power  or  resistances  are  avoided.  By  means  of  a 
belt  passing  over  the  wheel  W  motion  may  be  communi- 
cated from  the  shaft  to  any  machinery  desirable. 

124.  Condensing-  and  Non-Condensing-  Engines.1  — 
Sometimes  steam,  after  it  has  done  its  work  in  the  cylin- 
der, is  conducted  through  the  exhaust-pipe  to  a  chamber 
Q,  'called  a  condenser,  where,  by  means  of  a  spray  of  cold 
water  introduced  through  a  pipe  T,  it  is  suddenly  con- 
densed. This  water  must  be  pumped  out  of  the  condenser 
by  a  special  pump,  called  technically  the  air-pump ;  thus 
a  partial- vacuum  is  maintained.  Such  an  engine  is  called 
a  condensing  engine.  The  advantage  of  such  an  engine  is 
obvious,  for  if  the  exhaust-pipe,  instead  of  opening  into  a 
condenser,  communicates  with  the  outside  air,  as  in  the 
non-condensing  engine,  the  steam  is  obliged  to  move  the 
piston  constantly  against  a  resistance  arising  from  atmos- 
pheric pressure  of  15  pounds  for  every  square  inch  of  the 
surface  of  the  piston.  But  in  the  condensing  engine  no 
resistance  arises  from  atmospheric  pressure,  and  so  with  a 
given  steam  pressure  in  the  boiler  the  effective  pressure 
on  the  piston  is  considerably  increased ;  hence,  condensing 
engines  are  usually  more  economical  in  their  working. 

1  The  terras,  low-pressure  and  high-pressure  engines,  are  not  distinctive  as  applied  to 
engines  of  the  present  day. 


152 


MOLECULAR  ENERGY.  —  HEAT. 


125.  Compound  Condensing-  Engine.  —  This  engine  has 
two  cylinders,  each  like  that  of  a  simple  engine.  One,  A  (Fig.  134), 
called  the  high-pressure  cylinder,  receives  steam  of  very  high  pressure 
directly  from  the  boiler.  The  steam,  after  it  has  done  work  in  this  cylinder, 
passes  through  the  steam-port  into  cylinder  B,  called  the  low-pressure 
cylinder.  Cylinder  B  is  larger  than  cylinder  A.  The  steam  which  enters 
cylinder  B  possesses  considerable  tension,  and  is  therefore  capable  of 
doing  considerable  work  under  suitable  conditions.  It  should  be  borne  in 
mind  that  in  order  that  steam  may  do  work  in  any  cylinder,  it  is  necessary 


Fig.  134. 

that  an  inequality  in  the  tension  of  the  steam  each  side  of  the  piston 
should  be  maintained;  just  as  an  inequality  of  level,  i.e.  a  head,  is  essen- 
tial to  water-power.  The  steam,  after  it  has  done  its  work  in  cylinder  B, 
passes  through  a  port  into  a  condenser  (not  represented  in  the  figure), 
where  it  is  suddenly  condensed  or  let  down  to  a  very  low  tension.  If  a 
vertical  glass  tube  were  led  from  the  condenser  to  a  vessel  of  mercury 
below,  the  mercury  would  ordinarily  stand  about  25  inches  high  in  the 
tube,  which  would  show  that  the  tension  of  the  steam  against  which  the 
steam  when  it  enters  cylinder  B  does  work,  is  only  about  one-sixth  of  an 
atmosphere.  Much  energy  is  economized  by  the  compound  engine. 

126.  The  Locomotive.  —  The  distinctive  feature  of  the  loco- 
motive engine  is  its  great  steam-generating  capacity,  considering  its  size 
and  weight,  which  are  necessarily  limited.  To  do  the  work  ordinarily 
required  of  it,  from  three  to  six  tons  of  water  must  be  converted  into 


H 
?l 

Ull 


<u 

•> 
^ 

K 
o 

o 

u 
C 


STEAM-ENGINE.  153 

steam  per  hour.  This  is  accomplished  in  two  ways :  viz.,  first,  by  a  rapid 
combustion  of  fuel  (from  a  quarter  of  a  ton  to  a  ton  of  coal  per  hour) ; 
second,  by  bringing  the  water  in  contact  with  a  large  extent  (about  800 
square  feet)  of  heated  surface.  The  fire  in  the  "  fire-box "  A  (Fig.  136, 
Plate  II.)  is  made  to  burn  briskly  by  means  of  a  powerful  draft 
which  is  created  in  the  following  manner:  The  exhaust  steam,  after  it 
has  done  its  work  in  the  cylinders  B,  is  conducted  by  the  exhaust-pipe  C 
to  the  smoke-box  D,  just  beneath  the  smoke-stack  E.  The  steam,  as  it 
escapes  from  the  blast-pipe  F,  pushes  the  air  above  it,  and  drags  by  fric- 
tion the  air  around  it,  and  thus  produces  a  partial  vacuum  in  the  smoke- 
box.  The  external  pressure  of  the  atmosphere  then  forces  the  air  through 
the  furnace  grate  and  hot-air  tubes  G,  and  thus  causes  a  constant  draft. 
The  large  extent  of  heated  surface  is  secured  as  follows :  The  water  of 
the  boiler  is  brought  not  only  in  contact  with  the  heated  surface  of  the 
fire-box,  but  it  surrounds  the  pipes  G  (a  boiler  usually  contains  about 
150).  These  pipes  are  kept  hot  by  the  heated  gases  and  smoke,  all  of 
which  must  pass  through  them  to  the  smoke-box  and  smoke-stack. 

The  steam-engine,  with  all  its  merits  and  with  all  the 
improvements  which  modern  mechanical  art  has  devised, 
is  an  exceedingly  wasteful  machine.  The  best  engine  that 
has  been  constructed  utilizes  only  about  twenty  per  cent  of 
the  heat-power  generated  by  the  combustion  of  the  fuel. 

QUESTIONS.  /ml 

1.  What  kind  of  engine  (i.e.  condensing  or  non-condensing)  is  that 
which  produces  loud  puffs?    What  is  the  cause  of  the  puffs  ?^ 

2.  Why  does  the  temperature  of  steam  suddenly  fall  as  .it  jaioves 
the  piston?  i 

3.  What  do  you  understand  by  a  ten  horse-power  stearn-erigine  ?  / 

4.  Upon  what  does  the  power  of  a  steam-engine  depend  ?      '  -'/*\ 

5.  Is  the  compound  engine  a  condensing  or  a  non-condensing. en- 
gine ?     Which  is  the  locomotive  engine  ? 

6.  The  area  of  a  piston  is  500  square  inches,  and  the  average"unbal- 
anced  steam  pressure  is  30  pounds  per  square  inch ;  what  is  the  total 
effective  pressure  ?     Suppose  that  the  piston  travels  30  inches  at  each 
stroke,  and  makes  100  strokes  per  minute,  allowing  40  per  cent  for 
wasted  energy,  what  power  does   the  engine   furnish,  estimated  in 
horse-powers  ? 


CHAPTER   VI. 
ELECTRICITY  AND  MAGNETISM. 

Section  I. 

INTRODUCTORY    EXPERIMENTS. 

No  other  department  of  Physics  presents  so  many  favorable  oppor- 
tunities for  individual  work  as  that  of  Electricity.  There  is  none  in 
connection  with  which  apparatus  sufficient  to  equip  a  laboratory  can  be 
provided  so  cheaply,  when  the  amount  of  work  which  can  be  done  with 
it  is  considered;  certainly  there  is  no  other  department  in  connection 
with  which  laboratory  work  is  so  indispensable  in  order  to  acquire  a  working 
knowledge  of  the  subject. 

127.  Apparatus  Required.  —  A  tumbler  f  full  of  water  into 
which  has  been  poured  two  or  three  tablespoonfuls  of  strong  sulphu- 
ric acid ;  a  strip  of  sheet-copper,  and  two  pieces  of  zinc, 
each  about  5  inches  long  and  1|  inches  wide.  The  pieces 
of  zinc  should  be  T\  of  an  inch  thick.  A  piece  of  No.  16 
copper  wire,  12  inches  long,  should  be  soldered  to  one  end 
of  each  piece  of  metal.  The  soldering  should  be  covered 
with  asphalt um  paint.  Also,  a  rod  of  Norway  iron,  6  inches 
long  and  ^  of  an  inch  in  diameter;  4  yards  of  No.  23  in- 
sulated copper  wire  ;  a  magnetic  needle,  6  inches  long,  nicely 
poised  on  a  fine  needle-point ;  some  fine  iron  turnings  ;  and 
two  double  connectors.  These  connectors  (Fig.  136)  serve 
to  connect  two  wires,  without  the  inconvenience  of  twisting 
them  together.  Wind  the  wire  closely,  with  the  exception 
of  about  10  inches  at  each  extremity,  around  the  iron-rod, 
1§r'  '  nearly  from  end  to  end,  in  two  or  three  layers,  as  the  case 
may  require.  Amalgamate  one  of  the  zincs  as  follows :  first  dip  the 
zinc,  with  the  exception  of  about  |  an  inch  at  the  soldered  end,  into 
the  acidulated  water;  then  pour  mercury  over  the  surface,  and  finally 
rub  the  surface  wet  with  mercury  with  a  cloth. 


INTRODUCTORY   EXPERIMENTS.  155 

Experiment  111.  —  Put  the  unamalgamated  (dark  colored)  zinc 
into  the  liquid.  Bubbles  of  gas  arise  from  the  zinc.  These  bubbles, 
Chemistry  (page  24)  teaches,  are  hydrogen  gas.  Put  the  copper  strip 
into  the  liquid,  but  do  not  allow  the  two  metals  or  their  wires  to 
touch.  Do  bubbles  rise  from  the  copper? 

Experiment  112.  —  Remove  the  metals,  and  allow  the  liquid  to 
become  clear.  Connect  their  wires  with  a  double  connector,  and  in- 
troduce both  metals  into  the  liquid,  about  1  inch  apart.  Hold  them 
perfectly  still  for  a  minute,  and  observe  whether  any  bubbles  escape 
from  the  copper. 

Bubbles  escaping  from  both  metals  make  it  appear  as  if  chemical 
action  were  taking  place  between  both  metals  and  the  liquid.  But 
experience  will  teach  you  that  the  appearance  is  deceptive,  as  you  will 
find  that  only  the  zinc  is  consumed. 

Experiment  113.  —  Put  the  amalgamated  (bright)  zinc  into  the 
liquid.  If  the  zinc  is  properly  amalgamated,  no  bubbles  will  rise 
from  it.  Do  you  discover  any?  If  so,  report  it  to  your  teacher. 

Experiment  114.  —  Put  the  copper  strip  into  the  liquid.  Do  not 
allow  the  metals  or  their  wires  to  touch.  Do  bubbles  rise  from 
either  metal  ?  Connect  their  wires.  Do  bubbles  now  rise  from  either 
metal? 

Lesson  learned :  —  An  amalgamated  zinc  is  not  acted 
on  by  the  liquid  unless  a  copper  strip  is  also  in  the 
liquid,  and  not  then  unless  the  metals  are  connected. 
If  then  we  would  at  any 
time  stop  the  action,  we 
have  only  to  disconnect 
the  metals. 

It  seems  that  the  wire 
connector  serves  a  very 
important  purpose.  Does 
it,  meantime,  possess  any 
unusual  properties  f. 

Fig.  137. 

Experiment  115.  —  Place  a  magnetic  needle  (Fig.  137)  near  your 
tumbler.  When  the  needle  conies  to  rest,  it  points  north  and  south. 


156  ELECTRICITY  AND   MAGNETISM. 

Place  the  connecting  wire  over  and  near  the  needle,  so  that  that  por- 
tion of  the  wire  which  is  over  the  needle  shall  have  a  northerly  and 
southerly  direction.  Does  the  needle  move?  Does  the  end  of  the 
needle  pointing  to  the  north  (called  the  north-seeking  pole  of  the 
needle)  move  toward  the  east  or  the  west  ?  Imagine  that  your  wire 
is  a  tube  through  which  there  is  flowing  a  liquid.  Turn  the  tumbler 
half  way  around,  so  that  the  current  in  that  portion  of  the  wire 
which  is  over  the  needle  shall  be  reversed.  Do  you  observe  any 
change  in  the  deflection  of  the  needle?  Next,  lower  that  portion  of 
the  wire  which  is  over  the  needle,  and  place  it  nearly  under  the 
needle.  Do  you  observe  any  change  in  the  deflection  of  the  needle? 

Lesson  learned :  —  (1)  The  wire  connector  does  pos- 
sess an  unusual  property.  It  is  capable  of  exercising  an 
unusual  form  of  force.  This  new  form  of  force  is  called 
electro-magnetic  force.  (2)  Although  we  have  no  positive 
evidence  that  anything  of  the  nature  of  a  fluid  flows 
through  the  wire,  yet  in  discussing  certain  phenomena, 
such,  for  example,  as  the  deflection  of  the  needle,  it  is 
extremely  convenient,  at  least,  to  imagine  that  a  current 
passes  through  the  wire.  Something  does  pass  through  the 
wire.  What  this  something  is,  physicists  have  not  deter- 
mined. They  have  merely  given  it  a  name  —  electricity. 

128.  Some  Technical  Terms.  —  Experiments,  not 
easily  performed  by  the  pupil,  show  that  the  current 
traverses  the  liquid  between  the  metals  at  the  same  time 
that  it  traverses  the  connecting  wire,  so  that  the  current 
makes  a  complete  circuit.  The  term  circuit  is  applied  to 
the  entire  path  along  which  electricity  flows,  and  the  wire 
through  which  it  flows  is  called  the  conductor.  Bringing 
the  two  extremities  of  the  wires,  or  other  parts  of  the 
circuit,  in  contact  (so  as  to  complete  the  circuit)  and 
separating  them,  are  called,  respectively,  closing  and  open- 
ing, or  making  and  breaking,  the  circuit.  Opening  a  circuit 


INTRODUCTORY   EXPERIMENTS.  157 

at  any  point,  and  filling  the  gap  with  an  instrument  of  any 
kind,  so  that  the  current  is  obliged  to  pass  through  it,  is 
called  introducing  an  instrument  into  the  circuit.  Our  ar- 
rangement of  acidulated  water  and  two  metals  is  called  a 
voltaic  cell,  and  the  two  metals  are  called  its  elements. 
A  series  of  cells  properly  connected  is  called  a  battery, 
though  this  term  is  frequently  applied  to  a  single  cell. 
The  free  extremities  of  the  wires  are  called  poles  or  elec- 
trodes, and  the  same  terms  may  be  applied  to  any  two 
points  of  contact  in  any  part  of  the  circuit. 

129.  Conductors  and  Non-Conductors. 

Experiment  116.  —  Will  every  substance  answer  for  a  conductor  ? 
Introduce  into  the  circuit  between  the  electrodes,  pieces  of  wood, 
paper,  cloth,  glass,  iron,  brass,  zinc,  lead ;  also,  a  drop  of  mercury  on  a 
glass  plate.  Place  the  connecting  wire  over  the  magnetic  needle,  and 
determine,  by  the  deflection  of  the  needle,  through  which  of  these 
substances  electricity  will  pass.  Those  substances  through  which 
electricity  passes  readily  are  called  good  conductors.  Substances 
through  which  electricity  passes  with  great  difficulty  are  called  bad 
conductors,  non-conductors,  or  insulators.  Are  metals  conductors  or 
non-conductors  ? 

130.  Direction  of  the  Current,  etc.  —  It  is  evidently 
necessary  in  describing  a  current  to  assign  it  a  direction. 

Electricians  have  universally  agreed,  for  the  purpose  of 
uniformity  and  convenience,  to  assume  that  in  such  a  cell 
as  described,  electricity  flows  from  the  zinc,  where  the 
chemical  action  takes  place,  through  the  liquid  to  the 
copper  element,  thence  through  the  wire  to  the  starting- 
point,  i.e.  the  zinc  element.  If  we  take  any  two  points  in 
a  circuit,  of  course  the  current  will  be  from  one  toward 
the  other.  The  former  point  is  said  to  be  positive  (+) 
with  reference  to  the  latter  point  which  is  said  to  be 
negative  (— ).  Which  is  the  positive  element  of  a  battery, 
the  zinc  or  the  copper  plate  ?  Which  electrode,  i.e.  the 


158 


ELECTRICITY  AND   MAGNETISM. 


free  end  of  the  wire  connected  with  the  zinc  plate,  or  the 
end  of  the  wire  connected  with  the  copper  plate,  is  posi- 
tive? 

Experiment  117.  —  Place  the  connecting-wire  over  the  magnetic 
needle,  in  such  a  manner  that  the  current  will  flow  northward  through 
that  section  of  the  wire  that  is  above  the  needle.  Then  reverse  the 
direction  of  the  current.  Finally,  place  the  wire  under  the  needle. 
In  each  different  position  verify  the  following  rule  for  determining 
the  direction  of  the  deflection  when  the  direction  of  the  current  is 
known. 

131.  Ampere's  Rule.  —  Imagine  yourself  to  be  swim- 

ming in  the  current,  and  with  (i.e. 
your  head  in  the  same  direction  as) 
the  current,  and  facing  (i.e.  look- 
ing up  or  down  according  as  the 
needle  is  above  or  below  you)  the 
needle ;  in  such  a  position  the 
north  pole  of  the  needle  is  always 
deflected  toward  vour  left. 

Fig.  138. 

132.  Galvanoscope.  —  The  magnetic  needle  serves  the 
purpose  of  determining  the  presence  of  a  current  in  a  wire. 
A  needle  used  for  this  purpose  is  called  a  galvano scope. 
Electricity  set  in    motion   by  a  voltaic   battery  is  called 
galvanic   or   voltaic   and    sometimes    current   or    dynamic 
electricity. 


POTENTIAL   AND   ELECTRO-MOTIVE   FORCE.  159 

Section  II. 

POTENTIAL   AND   ELECTRO-MOTIVE  FORCE. 

133.  Potential.  —  In  order  that  water  may  flow  from 
one   vessel  A  to  another  B    through  a  connecting   pipe, 
there  must  be  a  difference  of  level  in  the  two  vessels ;  i.e. 
in  ordinary  language  there  must  be  a  head  of  water  in  A. 
The  head  of  water  in  A  causes  a  greater  pressure  at  the 
end  of  the  pipe  next  this  vessel  than  at  the  end  next  B, 
and  this  unbalanced  force  causes  a   flow  of  water  from 
A  to  B  until  there  is  the  same  level  in  both  vessels.    So, 
in  order  that  there  may  be  a  flow  of  electricity  from  a 
body  A  to  a  body  B,  or  from  a  given  point  A  in  a  body 
to  another  given  point  B  in  the  same  body,  there  must 
be  a  difference  of  electrical  condition  between  A  and  B. 
This  difference  of  condition  may  be  imagined  as  a  differ- 
ence of  electrical  pressure  and  is  called   a    difference  of 
electrical  potential. 

In  any  case  we  may  say  that  difference  of  potential  with 
reference  to  electricity  is  analogous  to  difference  of  pres- 
sure in  fluids,  and  that  electricity  always  tends  to  flow 
from  places  of  high  to  places  of  low  potential. 

134.  Electro-Motive  Force.  —  When  two  conductors 
are  connected  by  a  wire  it  is  found  that  the  rate  at  which 
electricity  passes  from  one  to  the  other  is  proportional  to 
the  difference  of  potential  of  the  two  conductors,  and  that 
this  is  proportional  to  the  work  that  would  be  expended 
in    carrying    a    unit    quantity    of    electricity    backwards 
through  the  wire.     So,  too,  in  any  circuit  it  is  found  that 
the  quantity  of  electricity  flowing  in  any  time  is  strictly 
proportional  to  the  amount  of  work  necessary  to  carry  a 


160  ELECTRICITY   AND    MAGNETISM. 

unit  quantity  of  electricity  backwards  through  the  circuit. 
This  important  magnitude  receives  the  name  electro-motive 
force  (E.M.F.),  although  it  is  apparent  that  it  is  not  a 
force.  The  E.M.F.,  or  work  done,  is  the  cause  of  difference 
of  potential. 

We  might  agree  to  call  any  point  in  a  liquid  stream 
positive  with  reference  to  all  points  below  it  or  of  lower 
level,  and  negative  with  reference  to  all  points  above  it, 
or  points  of  higher  level.  So  any  point  in  an  electrical 
conductor  is  said  to  be  positive  with  reference  to  all  points  of 
lower  potential,  and  negative  with  reference  to  all  points  of 
higher  potential. 

Is  there  such  a  thing  as  a  difference  of  electrical  condition  f 


Fig.  139. 

Experiment  118.  —  Separate  a  little  way  the  two  conductors  C  and 
D  (Fig.  139),  of  a  Holtz  machine.  Hold  two  pith  balls  suspended 
by  white  silk  threads  against  one  of  the  conductors  and  turn  the 
plate  a  few  times.  Remove  the  pith  balls  and  hold  them  near  each 
other.  They  repel  each  other.  Next  place  one  of  the  pith  balls  in 
contact  with  one  of  the  conductors  and  the  other  pith  ball  in  contact 
with  the  other  conductor.  Turn  the  plate  as  before,  remove  the  pith 
balls,  and  hold  them  near  each  other.  Now,  in  the  first  case,  the  two 


POTENTIAL   AND   ELECTRO-MOTIVE   FORGE.  161 

pith  balls  were  placed  in  contact  with  the  same  conductor,  and  hence 
acquired  the  same  electrical  condition  (i.e.  potential)  as  that  con- 
ductor. In  this  condition  they  repel  each  other.  But  after  being 
in  contact  with  different  conductors,  as  in  the  second  case,  they  at- 
tract each  other  (Fig.  140). 
Hence,  we  conclude  that  the 
two  conductors  are  in  a  dif- 
ferent electrical  condition. 

It  is  in  consequence  of 
this  difference  elf  elec- 
trical condition,  which 
always  exists  between 
such  bodies,  that  the 
electricity  passes  from 

one    conductor    through  Fig.  140. 

the  air  to  the  other,  rendering  the  air  in  its  path  tem- 
porarily luminous.  The  most  convenient  test  of  the 
electro-motive  force  of  an  electrical  machine  is  the  length 
of  spark  it  gives. 

135.    Electro-Chemical  Series. 

Experiment  119.  —  Take  two  plates  of  zinc,  either  both  amalga- 
mated or  both  unamalgamated,  connect  them,  put  them  into  acidu- 
lated water,  and  place  the  connecting  wire  over  a  magnetic  needle. 
Does  the  galvanoscope  show  that  there  is  a  current  in  the  wire  ?  Is 
there,  then,  a  difference  of  potential  between  the  two  plates  ? 

It  is  important  that  only  one  of  the  two  elements  of  a  vol- 
taic cell  should  be  acted  upon  by  the  liquid.  The  greater 
the  disparity  between  the  two  solid  elements,  with  reference 
to  the  action  of  the  liquid  on  them,  the  greater  the  difference 
in  potential ;  hence,  the  greater  the  current.  In  the  follow- 
ing electro-chemical  series  the  substances  are  so  arranged 
that  the  electro-positive,  or  those  most  affected  by  dilute 
sulphuric  acid,  are  at  the  beginning;  while  the  electro- 


162  ELECTRICITY   AND   MAGNETISM. 

negative,  or  those  least  affected  by  the  acid,  are  at  the, 
end.  The  arrow  indicates  the  direction  of  the  current 
through  the  liquid. 

+  "s    §   .s    1    I  I   I   I" 


It  will  be  seen  that  zinc  and  carbon  are  the  two  sub- 
stances best  adapted  to  give  a  strong  current. 

The  essential  parts  of  a  galvanic  cell  are  a  liquid  and  two 
different  conductors,  one  of  which  is  more  readily  acted 
upon  chemically  by  the  liquid  than  the  other. 

136.    Importance  of  Amalgamating  the  Zinc.  —  All 

commercial  zinc  contains  impurities,  such  as  carbon,  iron, 
etc.  Figure  141  represents  a  zinc  element  having  on  its 
surface  a  particle  of  carbon  a,  purposely  magnified.  If 
such  a  plate  is  immersed  in  dilute  sulphuric 
acid,  the  particles  of  carbon  will  form  with  the 
zinc  numerous  voltaic  circuits,  and  a  transfer 
of  electricity  along  the  surface  will  take  place. 
This  coasting  trade,  as  it  were,  between  the 
zinc  and  the  impurities  on  its  surface,  diverts 
so  much  from  the  regular  battery  current,  and 
thereby  weakens  it.  In  addition  to  this,  it 
Fig.  141.  occasions  a  great  waste  of  chemicals,  because, 
when  the  regular  circuit  is  broken,  this  local  action, 
as  ifc  is  called,  still  continues.  If  pure  zinc  were  used 
(formerly  it  was  used),  no  local  action  would  occur  at 
any  time,  and  there  would  be  no  consumption  of  chemi- 
cals, except  when  the  circuit  is  closed.  If  mercury  is 
rubbed  over  the  surface  of  the  zinc,  after  the  latter  has 
been  dipped  into  acid  to  clean  its  surface,  the  mercury 


POTENTIAL   AND   ELECTRO-MOTIVE   FORCE.  163 

dissolves  a  portion  of  the  zinc,  forming  with  it  a  semi- 
liquid  amalgam  which  covers  up  its  impurities,  and  the 
amalgamated  zinc  then  comports  itself  like  pure  zinc. 

137.  How  Electric  Energy  Originates.  —  According 
to  the  doctrine  of  the  conservation  of  energy,  whenever 
any  new  form  of  energy  is  generated  it  is  always  at  the  ex- 
pense of  some  other  form  of  energy ;  in  other  words,  some 
other  form  of  energy  is  transformed  into  the  new  form. 
When,  as  in  Experiment  118,  you  turn  the  plate  of  a 
Holtz  machine,  you  feel  a  peculiar  resistance  that  is  not 
wholly  due  to  the  friction  of  the  parts.  The  mechanical 
energy  which  you  expend  in  overcoming  friction  is  con- 
verted into  heat  energy.  The  mechanical  energy  which 
you  expend  in  overcoming  the  peculiar  resistance  is  trans- 
formed into  electric  energy. 

We  are  already  familiar  with  the  fact  that  the  chemical 
potential  energy  in  a  lump  of  coal  is  converted  during  the 
process  of  combustion  into  heat  energy.  When  zinc  is 
placed  in  acidulated  water,  a  similar  combustion  occurs, 
and  if  a  thermometer  is  placed  in  the  liquid,  it  will  show 
a  rise  of  temperature  as  the  burning  progresses.  If,  how- 
ever, the  zinc  is  connected  with  the  copper,  or  some  other 
suitable  element,  there  is  less  heat  generated  by  the  com- 
bustion, because  a  portion  of  the  chemical  potential  energy 
is  converted  into  electric  energy.  Electric  energy  origi- 
nates in  a  voltaic  cell  from  the  conversion  of  chemical 
potential  energy  into  this  form  of  energy. 


164  ELECTRICITY   AND   MAGNETISM. 

Section  III. 

BATTERIES. 

138.  Polarization  of  Elements.  —  If  you  connect  any 
voltaic  cell  with  a  sensitive  galvanoscope,  such  as  will  be 
described  hereafter,  you  will  find  that  in  a  few  minutes 
after  making  the  connection,  the  deflection  diminishes 
somewhat.  This  is  due  to  the  collection  of  hydrogen  at 
the  electro-negative  plate.  The  effect  of  the  hydrogen  is 
to  raise  the  potential  of  this  element  and  thereby  diminish 
the  difference  of  potential  between  the  two  plates.  What- 
ever tends  to  diminish  the  difference  of  potential  between 
the  two  elements,  tends  to  diminish  the  current  of  electric- 
ity, and  to  that  extent  to  diminish  the  value  of  a  voltaic 
cell.  This  action  is  called,  technically,  polarization  of  the 
elements.  Among  the  different  methods  that  have  been 
devised  for  remedying  this  evil,  the  most  efficient  is  that 
in  which  the  hydrogen  is  disposed  of  by  surrounding  the 

electro-negative  element  with  a 
liquid  with  which  the  hydrogen 
will  readily  enter  into  combina- 
tion. A  good  illustration  of  this 
method  may  be  found  in  the  ac- 
tion of  the  Bunsen  battery. 


139.      Bunsen    Battery. —The 

metal  employed  for  the  electro-positive 
plate  in  this,  as  in  nearly  all  batteries,  is 
zinc.  The  zinc  is  immersed  in  sulphuric 
acid  diluted  with  about  ten  times  its  volume 
Fig.  142.  of  water.  Inside  of  the  hollow  cylindrical 

zinc  plate  (Fig.  142)  is  a  cup  of  porous  unglazed  earthenware.  This  cup  con- 
tains a  liquid  composed  of  a  saturated  solution  of  potassium  bichromate, 


BATTERIES. 


165 


or  (better)  sodium  bichromate,  mixed  with  one-sixth  its  volume  of  sulphu- 
ric acid.  This  cup  serves  to  keep  the  two  liquids  separate,  but  does  not 
prevent  electrical  action.  In  this  cup  is  placed  a  bar  of  carbon,  which  is 
the  electro-negative  plate.  The  larger  portion  of  the  hydrogen  generated 
by  the  action  between  the  zinc  and  the  acidulated  water  enters  into  com- 
bination with  some  of  the  constituents  of  the  bichromate  of  potash,  and 
thereby  prevents  in  a  large  measure  -the  polarization  of  the  electro- 
negative element.  Such  a  battery  is  called  a  two-fluid  battery. 

14O.  Grenet  Battery.  —  In  this  battery  a  small  flat  plate  of  zinc, 
2  (Fig.  143)  is  suspended  between  two  carbon  plates,  CC.  The  carbons  re- 
main in  the  liquid  all  the  time.  The  zinc  should  be  drawn  up  out  of  the 
liquid  by  means  of  a  slide  rod  a  when  the  battery  is  not  in  use,  as  a 
broken  circuit  does  not  prevent  the  consumption  of  the  zinc  when  it  is  in 
the  liquid,  even  though  the  zinc  is  well  amalgamated. 
a 


Fig.  143.  Fig.  144. 

This  battery  gives  a  more  energetic  current  for  a  short  time  than  the 
Bunsen  battery,  but  the  carbon  in  this  battery  becomes  sooner  polarized, 
and  the  liquid  sooner  exhausted  than  in  the  Bunsen  battery.  It  is  an 
extremely  convenient  and  popular  battery  for  brief  schoolroom  use,  as  it 
is  very  energetic  in  its  action  and  requires  little  care. 

141.  Daniell  Battery.  —  One  of  the  chief  virtues  of  this  battery 
(Fig.  144)  is,  that  it  polarizes  less  than  most  other  kinds  of  batteries,  and 
therefore  gives  a  more  constant  current.  The  zinc  is  suspended  in  a 


166  ELECTRICITY    AND   MAGNETISM. 

porous  cup,  either  in  pure  water,  or  in  water  to  which  has  been  added  a 
little  zinc  sulphate  to  hasten  the  action  when  the  battery  is  first  set  up. 
The  zinc  is  not  amalgamated.  Outside  the  cup  is  a  thin  sheet  of  copper 
in  the  form  of  a  hollow  cylinder  immersed  in  a  saturated  solution  of 
copper  sulphate.  In  a  pocket  near  the  top  of  the  copper  sheet  are  kept 
lumps  of  copper  sulphate,  which  are  gradually  dissolved  to  take  the  place 
of  that  which  is  consumed  by  the  action  of  the  battery.  This  battery 
requires  very  little  attention,  and  is  largely  used  in  England  for  tele- 
graphing. 


Section  IV. 

SOME  EFFECTS   PRODUCED   BY  AN  ELECTRIC   CURRENT. 

142.  Heating  and  Luminous  Effects. 

Experiment  120.  —  Connect  six  or  eight  Bunsen  (or  Grenet  cells) 
abreast  (see  page  186).  Attach  connectors  to  the  electrodes,  and  intro- 
duce between  the  connectors  a  piece  of  N"o.  30  platinum  wire,  less  than 
half  an  inch  long.  The  platinum  wire  is  heated  to  a  luminous  state. 
Place  the  platinum  wire  over  a  gas  burner,  turn  on  the  gas,  and 
light  it  by  the  heat  of  the  wire.  This  illustrates  one  of  the  practical 
uses  to  which  the  electric  current  is  put  in  lighting  numerous  gas 
burners  in  halls  and  theatres.  Remove  the  platinum  wire,  and  intro- 
duce into  the  circuit  an  incandescent  lamp  of  from  four  to  six 
candle-power.  Does  this  arrangement  of  battery  render  the  carbon 
filament  luminous? 

Experiment  121.  —  Connect  the  eight  cells  in  series  (see  page  187), 
and  introduce  the  same  lamp  into  the  circuit.  Does  the  filament 
become  luminous  ?  Remove  the  lamp  from  the  circuit,  and  insert  the 
platinum  wire  as  before.  Does  the  platinum  wire  become  as  hot  as 
in  the  former  arrangement  of  cells  ?  Which  arrangement  gives  the 
greater  heating  effect  with  the  platinum  wire?  Which  with  the 
lamp? 

143.  Chemical  Effects. 

Experiment  122. —  Take  in  a  test-tube  a  quantity  of  an  infusion  of 
purple  cabbage  (the  cabbage  may  be  found  at  a  suitable  time  of  the 


EFFECTS   PRODUCED   BY   AN   ELECTRIC   CURRENT.      167 

year  in  any  market)  prepared  by  steeping  its  leaves  until  well  cooked. 
Pour  into  this  infusion  a  few  drops  of  any  alkali,  such  as  a  solution 
of  caustic  soda.  The  infusion  is  changed  thereby  from  a  purple  to  a 
green  color.  In  another  test-tube  take  another  portion  of  the  purple 
infusion.  Into  this  pour  a  few  drops  of  any  acid,  such  as  dilute  sul- 
phuric acid.  The  purple  is  changed  to  a  red.  Only  acids  will  turn 
this  infusion  to  a  red  and  only  alkalies  will  turn  it  to  a  green.  Into  a 
rather  strong  solution  of  sodium  sulphate  pour  enough  of  the  purple 
infusion  to  give  it  a  decided  color. 

'   Four  some  of  this   colored   solution   into   a  Y-shaped  glass  tube 
(Fig.  145).    Take  two  short  pieces  of  copper  wire  covered  with  rubber 
and  having  strips  of  platinum  soldered  upon  one 
of  their  ends  for  electrodes,  and  introduce  one  of 
these  electrodes  into  each   arm  of   the  tube  until 
it  nearly  reaches  the  bottom  or  angle  of  the  V. 
By  means  of  connectors   connect  the  battery  (of 
three  cells  in  series)  wires  with  the  free  extremities 
of  these  wires.     The  liquid  between  the  two  plati- 
num electrodes  forms  a  part  of  the  circuit,  so  that 
the  current  of  electricity  passes  through  this  por- 
tion of  the  liquid.      Soon  the  liquid  around  the  Fig.  145. 
—  electrode  is  turned  green,  while  that  around  the 
+  electrode  is  turned  red.     Evidently,  decomposition  of  the  sodium  sul- 
phate has  taken  place.     An  acid  and  an  alkali  are  the  results. 

A  substance  that  may  be  decomposed  by  electricity  is 
called  an  electrolyte,  and  the  process  electrolysis.  An  elec- 
trolyte must  be  a  compound  substance,  and  in  a  liquid  state. 
When  a  salt  (see  Chemistry,  page  54)  is  electrolyzed,  the 
base  appears  at  the  —pole,  and  the  acid  at  the  -f  pole. 

Experiment  123. —  Wet  a  piece  of  writing  paper  with  a  liquid 
prepared  in  the  following  manner.  Dissolve  by  heating  about  three 
grains  of  pulverized  potassium  iodide  in  about  a  tablespoonful  of 
water.  Make  a  paste  by  boiling  pulverized  starch  in  water.  Take  a 
portion  of  this  paste  about  the  size  of  a  pea,  stir  it  into  the  solution. 
Spread  the  wet  paper  smoothly  on  a  piece  of  tin,  e.g.  on  the  bottom 
of  a  tin  basin.  Press  the  —  pole  of  your  battery  against  an  uncov- 
ered part  of  the  tin.  Draw  the  +  pole  over  the  paper.  A  mark  is 


168 


ELECTRICITY   AND   MAGNETISM. 


produced  upon  the  paper  as  if  the  pole  were  wet  with  a  purple  ink. 
In  this  case  the  potassium  iodide  is  decomposed,  and  the  iodine  com- 
bining with  the  starch  forms  a  purplish  blue  compound. 

In  the  experiment  with  the  cabbage  infusion  you  proba- 
bly discovered  bubbles  of  gas  arising  from  this  liquid,  caus- 
ing a  foam.  This  is  evidence  that  there  was  another  de- 
composition going  on  besides  that  of  the  sodium  sulphate 
—  a  sort  of  double  decomposition.  We  will  now  take 
measures  to  collect  these  gases  for  examination. 

Experiment  124.  —  Take  a  dilute  solution  of  sulphuric  acid  (1 
part  by  bulk  to  20),  pour  some  of  it  into 
the  funnel  (Fig.  146),  so  as  to  fill  the 
U-shaped  tube  when  the  stoppers  are  re- 
moved. Place  the  stoppers  which  support 
the  platinum  electrodes  tightly  in  the 
tubes.  Connect  with  these  electrodes  the 
battery  wires.  Instantly  bubbles  of  gas 
arise  from  both  electrodes,  accumulating 
in  the  upper  part  of  the  tube  and  forcing 
the  liquid  back  into  the  tunnel.  Twice 
as  much  gas  arises  from  the  —electrode 
as  from  the  +  electrode.  Close  the  pas- 
sage in  the  rubber  tube  by  turning  down 
the  screw  of  the  pinch-cock  a.  Light  a 
splinter  of  fine  wood,  blow  out  the  flame, 
leaving  it  glowing;  remove  the  stopper 
holding  the  +  electrode  and  introduce  the 
glowing  splinter  into  the  gas  in  this  arm 
of  the  tube.  It  relights  and  burns  vigor- 
ously, showing  that  the  gas  is  oxygen. 
Fig.  146.  (See  Chemistry,  page  19.)  Platinum  elec- 

trodes are  used,  otherwise  a  portion  of  the  oxygen  carried  to  the 
-f  electrode  would  not  be  set  free,  but  would  oxydize  the  metal  (e.g. 
copper),  instead  of  appearing  as  a  gas  in  this  arm  of  the  tube.  Fill 
this  arm  of  the  tube  with  water  and  stopper  it.  Invert  the  U-tube ; 
the  gas  in  the  other  arm  of  the  U-tube  collects  in  the  bend  of  the 
tube  and  in  the  small  branch  tube.  Light  a  match,  remove  the 


EFFECTS    PRODUCED    BY   AN    ELECTRIC    CURRENT.      169 


rubber  tube,  and  quickly  hold  the  match  at  the  orifice  of  the  branch 
tube.  The  gas  burns.  (See  Chemistry,  page  25.)  It  is  hydrogen. 
This  operation  is  commonly  called  "  decomposing  water  by  electric- 
ity." See  if  you  can  "  decompose  water  "  with  your  battery  of  three 
cells  connected  abreast. 

Experiment  125.—  This  delightful  experiment  may  be  performed 
by  the  teacher,  or  an  experienced  pupil,  before  the  class.  Take  about 
one-fourth  of  a  teacupful  of  water, 
dissolve  in  it  about  two  grams  of 
silver  nitrate.  Do  not  wet  the  hands 
with  the  solution,  as  it  will  stain 
them  black.  Nearly  fill  the  electrol- 
ysis tank  (Fig.  147)  which  accom- 
panies the  porte-lumiere  (page  310). 
Arrange  a  battery 
of  two  cells  in 
series.  Place  the 
tank  in  position 
in  the  porte-lu- 
miere to  project 
it  on  a  screen 
in  a  dark  room. 
Connect  the  bat- 
tery wires  with 
the  electrodes  in 
the  tank.  A  beau- 
tiful deposit  of  silver  will  be  made 
therefrom  toward  the  +  electrode,  and  bearing  a  strong  resemblance  to 
vegetable  growth ;  hence  it  is  called  the  "  silver  tree."  In  Figure  148, 
A  represents  a  silver  tree  deposited  from  a  weak  solution  and  B 
from  an  extremely  weak  solution. 

144.    Physiological  Effects. 

Experiment  126.  —  Take  a  single  Bunsen  cell  and  place  its  elec- 
trodes each  side  of  the  tip  of  the  tongue.  A  slight  stinging  (not 
painful)  sensation  is  felt,  followed  by  a  peculiar  acrid  taste. 

When  a  battery  is  known  not  to  be  very  powerful,  the 
tongue  serves  as  a  convenient  galvanoscope  to  determine 
whether  the  battery  is  in  working  condition. 


Fig;  147. 


on 


Fig.  148. 

the  —electrode,  spreading 


170  ELECTRICITY    AND    MAGNETISM. 

145.    Magnetic  Effects. 

Experiment  127.  —  Take  the  iron  rod  having  an  insulated  wire 
wound  around  it,  and  connect  the  extremities  of  the  wire  with  the 
battery  wires ;  in  other  words,  introduce  this  wire 
into  the  circuit.  Bring  a  nail  (Fig.  149)  or  other 
piece  of  iron  near  one  end  of  the  rod.  The  rod  at- 
tracts the  nail  with  considerable  force,  and  this 
nail  will  attract  other  nails.  The  rod  has  all  the 
properties  of  a  magnet,  as  will  be  seen  hereafter. 
Break  the  circuit.  The  iron  rod  instantly  loses 
its  magnetic  force,  and  the  nails  drop. 

The  iron  rod  is  called  a  core,  the  coil  of  wire  a 
helix,  and  both  together  an  electro-magnet.  In  order 
to  take  advantage  of  the  attraction  of  both  ends 
or  poles  of  the  magnet,  the  rod  is  most  frequently 
bent  into  a  U-shape  (A,  Fig.  150),  and  then  it  is 
called  a  horse-shoe  magnet.  More  frequently  two 
c  iron  rods  are  used,  connected  by  a  rectangular 

piece  of  iron,  as  a  in  B  of  Figure  150.  The  method 
of  winding  is  such  that  if  the  iron  core  of  the  horse-shoe  were 
straightened,  or  the  two  spools  were  placed  together  end  to  end, 

one  would  appear  as  a  contin- 
uation of  the  other.  A  piece  of 
soft  iron,  &,  placed  across  the 
ends  and  attracted  by  them,  is 
called  an  armature.  The  piece 
Fig.  150.  Of  jron)  a>  is  called  a  yoke. 

Experiment  128.  —  Arrange  a  battery  of  four  cells  in  series.  In- 
troduce into  the  circuit  an  electro-magnet  wound  with  a  long,  fine 
wire  (having  a  resistance  of  not  less  than  25  ohms.1  Ascertain 
approximately  the  force  required  to  pull  an  armature  {e.g.  a  large 
nail)  off  the  poles. 

Next  remove  this  electro-magnet,  and  introduce  into  the  circuit  in 
its  place  an  electro-magnet  wound  with  coarse  wire  (which  has  a 
resistance  not  exceeding  1  ohm).  See,  by  pulling,  with  what  force  it 
holds  a  nail  on  one  of  its  poles. 

Experiment  129.  —  Arrange  a  battery  of  four  cells  abreast.  In- 
troduce into  the  circuit  the  fine  wire  magnet.  See  with  what  force  it 

1  See  page  178. 


ELECTRICAL   MEASUREMENTS.  171 

holds  its  armature.     Which  arrangement  of  cells  produces  the  greater 
magnetic  power  with  this  electro-magnet? 

Next  introduce  in  its  place  the  low-resistance  electro-magnet  and 
find  with  what  force  it  holds  the  nail.  Which  arrangement  of  cells 
produces  the  greater  magnetic  power  in  this  magnet  ? 

Important  Lesson :  The  results  of  our  experiments 
thus  far  teach,  that  the  arrangement  of  a  battery  of  several 
cells  and  the  apparatus  used  should  be  adapted  to  each  other. 

It  is  apparent  that,  if  there  are  rules  or  laws  which  will  enable  a  person 
who  would  use  an  electric  current  for  experimental  or  industrial  purposes, 
to  determine  by  calculation  just  what  is  the  best  method  of  arrangement 
in  any  given  case,  it  is  of  the  utmost  importance  that  these  laws  should 
be  understood. 


Section  V. 

ELECTRICAL    MEASUREMENTS. 

The  wonderful  developments  which  have  been  made  in  recent  years 
in  electrical  science,  and  which  have  led  to  the  employment  of'  electric 
energy  in  connection  with  a  great  diversity  of  industrial  arts,  are  almost 
wholly  due  to  a  better  understanding  of  what  electrical  measurements  can 
be  made,  and  how  to  make  them.  Indeed,  little  of  a  practical  nature  can 
be  done  without  some  acquaintance  with  the  methods  of  making  these 
measurements. 

146.  Some  Technical  Terms.  —  A  quantity  of  water 
may  be  measured  either  in  quarts  or  pounds ;  i.e.  by  its 
volume  or  weight.  Although  electricity  has  neither  vol- 
ume nor  weight,  yet  it  has  that  which  answers  strictly  to 
the  term  quantity,  and  the  quantity  can  be  measured  by 
suitable  means.  The  unit  employed  for  the  measurement 
of  a  quantity  of  electricity  is  called  a  coulomb.  A  stream  of 
water  flowing  through  a  pipe  might  be  described  by  stating 
the  number  of  quarts  which  flow  through  the  pipe,  or  past 


172  ELECTRICITY   AND   MAGNETISM. 

any  point  in  the  pipe,  in  a  minute.  In  a  similar  manner, 
we  describe  an  electric  current  by  stating  the  number  of 
coulombs  that  pass  through  a  conductor,  or  that  pass  a 
given  point  of  a  conductor,  in  a  second. 

The  quantity  of  electricity  passing  through  a  conductor 
in  a  given  time,  in  other  words  the  rate  of  flow,  determines 
the  strength  of  the  current.  When  the  quantity  passing 
is  one  coulomb1  per  second,  the  strength  of  the  current  is 
said  to  be  one  ampere.  A  current  of  10  coulombs  per 
second  has  a  strength  of  10  amperes.  The  arapdre  is  the 
unit  for  measuring  current  strength.  There  is  no  unit 
analogous  to  this  for  measuring  liquid  currents.  It  should 
be  observed  that  the  term  strength  refers  only  to  the 
quantity  of  electricity  passing,  and  not  to  the  energy  of  the 
current. 

As  we  might  calculate  the  energy  of  a  current  of  water 
by  multiplying  the  weight  of  water  falling  by  the  distance 
it  falls,  so  if  we  represent  by  C  the  strength  of  current  in 
amperes,  and  by  V  the  electro-motive  force  or  difference  of 
potential  in  volts  (see  next  paragraph),  then 

CV  =  energy  of  current, 

which  is  expressed  in  a  unit  called  an  ampere-volt  (or  watt), 
much  as  we  express  mechanical  energy  in  foot-pounds. 
This  amount  of  energy  per  second  is  equivalent  to  about 
7^g-  horse-power. 

From  this  formula  we  infer  that  when  the  electro-motive 
force  remains  the  same,  the  energy  of  a  current  varies  as 
its  strength ;  and  when  the  current  strength  does  not 
change,  the  energy  varies  as  the  electro-motive  force.  As 
indicated  above,  difference  of  potential  and  electro-motive 
force  are  measured  in  a  unit  called  a  volt.  For  our  pur- 

1 A  coulomb  is  the  quantity  of  electricity  delivered  by  a  one-ampere  current  in  one  second. 


C.G.S.    MAGNETIC    AND   ELECTRO-MAGNETIC   UNITS.     173 

pose  it  will  answer  to  consider  a  volt  as  the  electro-motive 
force  of  a  Daniell's  cell ;  i.e.  it  is  about  the  difference  of 
potential  between  the  zinc  and  the  copper  of  this  cell. 


Section  VI. 

C.G.S.   MAGNETIC   AND   ELECTRO-MAGNETIC   UNITS. 

[This  section  is  intended  to  assist  the  student  who  is  ambitious  to  read 
technical  works  on  electricity,  but,  like  other  matter  in  fine  print,  it  is  not 
included  in  the  course  of  study  prescribed  in  this  book.] 

147.  Magnetic    Units.  —  These  units  are  based  on  the   forces 
exerted  between  two  magnetic  poles.     They  form  the  basis  for  the  electri- 
cal units  adopted  by  the  Congress  of  Electricians,  held  at  Paris  in  1871. 

Unit  Magnetic  Pole.  —  A  unit  magnetic  pole  is  one  which  repels  a  similar 
pole  placed  at  a  distance  of  lcm  with  a  force  of  1  dyne.  It  has  no  special 
name ;  its  dimensions  are  M^L^T^1. 

Unit  of  Intensity  of  a  Magnetic  Field. — The  intensity  of  a  magnetic 
field  is  one  C.G.S.  unit  when  the  force  which  acts  on  a  unit  magnetic  pole 
in  this  field  is  1  dyne.  Its  dimensions  are  M-^L^T-1. 

148.  Electro-Magnetic  Units  and  Practical  Units.— 

Unit  of  Current  Strength:  —  A  current  has  the  strength  of  one  C.G.S.  unit, 
if,  in  passing  through  a  circuit  lcm  long,  bent  into  the  form  of  an  arc  of  a 
circle  of  lcm  radius  (so  as  to  be  always  lcm  away  from  the  magnet-pole), 
it  exerts  a  force  of  1  dyne  on  a  unit  magnet-pole  placed  at  the  center. 

Unit  of  Quantity :  —  The  quantity  of  electricity  which  passes  through  a 
circuit  in  one  second  when  the  strength  of  the  current  is  one  C.G.S.  unit. 

Unit  of  Electro-motive  Force :  —  The  E.M.F.  necessary  in  order  that  a  unit 
of  quantity  may  do  the  work  of  an  erg.  [W  =  QE.] 

Unit  of  Resistance:  —  A  conductor  has  a  resistance  of  one  C.G.S.  unit 
when  a  unit  difference  of  potential  between  its  two  ends  causes  a  unit  of 
current  to  pass  through  it. 

Inasmuch  as  in  practice  the  employment  of  these  units  leads  to  the  use 
of  very  large  numbers,  units  have  been  adopted  which  are  decimal  multi- 
ples of  the  C.G.S.  units.  They  have  received  special  names  and  are 
known  as  the  practical  units. 


174 


ELECTRICITY   AND   MAGNETISM. 


TABLE  OF  ELECTRO-MAGNETIC  UNITS. 


QUANTITIES. 

SYMBOL. 

1 

NAME   OP 
PRACTICAL 
UNITS. 

NO.OFC.G.S. 
UNITS  IN 
ONE  PRAC- 
TICAL UNIT. 

DIMENSIONS  OP  UNIT. 

Resistance  .... 

R 

Ohm 

10» 

LT-1 

Electro-motive  force 

E 

Volt 

108 

M*L*T-2 

Current  Strength 

C 

Ampere 

10-1 

M*L*T-i 

Quantity     .... 

Q 

Coulomb 

10-1 

M*L* 

Section  VII. 

GALVANOMETERS. 

149.    Introductory  Experiments. 

Experiment  130.  —  Wind  a  battery  wire  lengthwise  once  around 
a  book,  and  place  the  book  either  above  or  below  and  near  to  a 
magnetic  needle,  and  hold  the  book  in  such  a  position  that  that  por- 
tion of  the  current  which  circulates  around  the  book  will  have  a 
northerly  and  southerly  direction.  Notice  the  extent  of  the  deflection 
of  the  needle.  Then  wind  the  wire  closely  20  or  30  times  around 
the  book,  and  hold  it  in  the  same  position,  and  at  the  same  distance 
from  the  needle  as  before.  The  needle,  now  that  the  current  is  carried 
several  times  past  it,  makes  a  larger  deflection;  consequently  the 
effect  of  several  windings  is  to  render  the  needle  more  sensitive  to 
weak  currents. 

Experiment  131.  —  Connect  two  cells  abreast,  and  once  more  hold 
the  book  with  its  many  turns  of  wire  near  the  needle,  as  in  the  last 
experiment.  The  deflection  is  larger  than  before,  which  is  due  to 
the  fact  that  the  two  cells  give  a  stronger  current  than  one  cell. 

It  thus  seems  that  a  galvanoscope,  in  addition  to  its  other 
uses,  may  indicate  the  strength  of  a  current,  and  when 
properly  constructed  to  measure  the  relative  strength  of 
currents  it  is  called  a  galvanometer. 


GALVANOMETERS.  175 

150.  Tangent  Galvanometer.  —  The  galvanometer  G, 
represented  in  Figure  151,  has  a  magnetic  needle  about 
•J  inch  long  and  an  indicator  of  light  aluminum  wire  about 
3.5  inches  long,  resting  upon  and  parallel  with  the  needle. 
The  whole  is  suspended  from  a  brass  frame  by  a  very  fine, 
untwisted,  silk  fiber,  just  over  a  coil  of  wire  such  as  was 
formed  by  winding  a  wire  about  the  book.     Between  the 
needle  and  coil  is  a  card  containing  a  circle  divided  into 
halves  by  a  diameter  parallel  with  the  wires  of  the  coil 
below.     Each  extremity  of  this  diameter  is  numbered  zero. 
Each  semicircle  is  divided  into  halves,  and  each  quarter 
circle  is  divided  into  ninety  degrees  and  numbered  each  way 
from  zero  to  the  ninetieth  degree.     The  whole  is  covered 
with  a  glass  case  to  prevent  disturbance  by  currents  of  air. 

When  the  needle  of  a  galvanometer  is  short  in  compari- 
son with  the  length  of  its  coil  the  strength  of  currents  varies 
as  the  tangents  of  the  angles  of  deflection.  Such  a  galvan- 
ometer is  called  a  tangent  galvanometer.  For  example, 
suppose  that  the  deflections  produced  in  the  same  tangent 
galvanometer  by  two  currents  are  80°  and  70°.  Consult- 
ing the  Table  of  Tangents  in  Appendix,  C,  we  find  the 
tangents  of  these  angles  are  respectively  5.67  and  2.75 ; 
hence  the  former  current  is  (5.67  -*-  2.75  =  )  2  +  times  as 
strong  as  the  latter. 

The  student  should  understand  that  the  galvanometer  described  above, 
is  not,  strictly  speaking,  a  standard  tangent  galvanometer.  The  manifold 
uses  to  which  galvanometers  are  put  in  a  physical  laboratory,  properly 
require  a  variety  of  instruments,  which  would  make  an  equipment  very 
expensive.  The  galvanometer  here  described  answers  very  well  all  the 
purposes  of  this  book.  The  results  obtained  by  its  use  are  approximately 
those  which  would  be  obtained  by  a  standard  tangent  galvanometer  of  the 
usual  form ,  in  which  the  needle  is  suspended  at  the  center  of  a  large  cir- 
cular coil  of  wire. 

151.  Galvanometer  with  an  Astatic  Needle. — This  needle 
is  much  more  sensitive  to  weak  currents  than  the  needle  described  above. 


176 


ELECTRICITY  AND   MAGNETISM. 


It  consists  of  two  magnetic  needles  fastened  to  a  common  axis,  but  having 
their  poles  reversed,  so  that,  for  example,  the  +  pole  of  one  is  over  the 
—  pole  of  the  other.  It  is  suspended  by  a  silk  fiber,  so  that  one  of  the 
needles  may  rotate  within  the  coil  while  the  other  rotates  above  the  coil. 
The  current  acts  upon  both  needles  to  turn  them  in  the  same  direction. 
Moreover  the  current  both  above  and  below  acts  in  the  same  direction  on 
the  needle  which  is  suspended  within  the  coil,  hence  the  astatic  needle  is 
much  more  sensitive  than  a  single  needle.  The  needle  does  not  point 
north  and  south  like  the  ordinary  needle,  but  more  nearly  east  and  west. 


Section  VIII. 

RESISTANCE   OF   CONDUCTORS. 

152.    External  Resistance. 

Experiment  132.  —  Introduce  into  a  circuit  a  galvanometer,  and 
note  the  number  of  degrees  the  needle  is  deflected.  Then  introduce 
into  the  same  circuit  the  wire  on  the  spool  numbered  4  on  the  plat- 
form, S  (Fig.  151).  (The  wire  on  any  one  of  the  five  spools  on  this 
platform  can  at  any  time  be  introduced  into  a  circuit,  by  connecting 
the  battery  wires  with  the  binding  screws  on  each  side  of  the  spool 
to  be  introduced.) 


Fig.  151. 

The  deflection  is  now  less  than  before.  The  copper  wire  on  this 
spool  is  16  yards  in  length;  its  size  is  No.  30  of  the  Brown  and 
Sharpe  wire  gauge.  When  this  spool  is  in  circuit,  the  circuit  is  16 
yards  longer  than  when  the  spool  is  out.  The  effect  of  lengthening 


RESISTANCE   OF   CONDUCTORS.  177 

the  circuit  is  to  weaken  the  current,  as  shown  by  the  diminished 
deflection. 

Experiment  133.  — Next,  substitute  Spool  2  for  Spool  4.  This 
contains  32  yards  of  the  same  kind  of  wire  as  that  on  Spool  4.  The 
deflection  is  still  smaller. 

The  weakening  of  the  current  by  introducing  these  wires  is  caused 
by  the  resistance  which  the  wires  offer  to  the  current,  much  as  the 
friction  between  water  and  the  interior  of  a  pipe  impedes,  to  some 
extent,  the  flow  of  water  through  it.  The  longer  the  pipe  the  greater 
is  the  resistance  to  the  flow. 

If  the  wire  on  the  spools  had  been  the  only  resistance  in  the  cir- 
cuit, then,  when  Spool  2  was  in  the  circuit,  the  resistance  of  the  circuit 
would  have  been  double  the  resistance  that  it  was  when  Spool  4  was 
in  the  circuit,  and  the  current,  with  double  the  resistance,  would  have 
been  half  as  strong. 

(1)  Other  things  being  equal,  the  resistance  of  a  conductor 
varies  as  its  length. 

Experiment  134.  —  Next  substitute  Spool  1  for  Spool  2.  This 
spool  contains  32  yards  of  No.  23  copper  wire,  —  a  thicker  wire  than 
that  on  Spool  2,  but  the  length  of  the  wire  is  the  same.  The  deflec- 
tion is  now  greater  than  it  was  when  Spool  2  was  in  circuit.  This 
indicates  that  the  larger  wire  offers  less  resistance. 

Careful  experiments  show  that  (2)  the  resistance  of 
all  conductors  varies  inversely  as  the  areas  of  their  cross 
sections.  Jf  the  conductors  are  cylindrical  it  varies  inversely 
as  the  square  of  their  diameters. 

Experiment  135.  —  Substitute  Spool  5  for  Spool  1,  and  compare 
the  deflection  with  that  obtained  when  Spool  4  was  in  the  circuit. 
The  deflection  is  smaller  than  when  Spool  4  was  in  circuit.  The  wire 
on  these  two  spools  is  of  the  same  length  and  size,  but  the  wire  of 
Spool  5  is  German  silver.  It  thus  appears  that  German  silver  offers 
more  resistance  than  copper. 

(3)  In  estimating  the  resistance  of  a  conductor,  the  specific 
resistance  of  the  substance  must  enter  into  the  calculation. 
(See  Table  of  Specific  Resistances,  Appendix,  D.) 


178  ELECTRICITY   AND   MAGNETISM. 

The  resistance  of  metal  conductors  increases  slowly  with 
the  temperature  of  the  conductor.  The  resistance  of  Ger- 
man silver  is  affected  less  by  changes  of  temperature  than 
that  of  most  metals ;  hence  its  general  use  in  standards  of 
resistance. 

153.  Internal   Resistance. 

Experiment  136.  —  Connect  the  copper  and  zinc  strips  used  in 
Experiment  114  with  the  galvanometer,  and  introduce  the  strips  into 
a  tumbler  nearly  full  of  acidulated  water.  Note  the  deflection.  Then 
raise  the  strips,  keeping  them  the  same  distance  apart,  so  that  less  and 
less  of  the  strips  will  be  submerged.  As  the  strips  are  raised,  the 
deflection  becomes  smaller.  This  is  caused  by  the  increase  of  resistance 
in  the  liquid  part  of  the  circuit,  as  the  body  of  liquid  lying  between 
the  two  strips  becomes  smaller.  The  resistance  of  the  liquid  part  of 
the  battery  is  called  internal  resistance,  in  distinction  from  that  of  the 
rest  of  the  circuit,  which  may  be  regarded  as  external  resistance. 

(4)  The  internal  resistance  of  a  circuit  varies  inversely 
as  the  area  of  the  cross  section  of  the  liquid  between  the  two 
elements. 

In  a  large  cell  the  area  of  the  cross  section  of  the  liquid 
between  the  elements  is  larger  than  in  a  small  cell,  con- 
sequently the  internal  resistance  is  less.  This  is  the  only 
way  in  which  the  size  of  a  cell  affects  the  current. 

154.  Measurement  of  Resistance ;    The  Ohm.  —  Re- 
sistance is  measured  by  a  unit  called  an  ohm.     An  ohm 
is  the  resistance  of  about  9  inches  of  No.  30  (B.  &  S.  G.) 
German  silver  wire,  or  about  9.3  feet  of  No.  30  copper 
wire  at  ordinar}r  temperature. 

155.  Description  of  the  Rheostat.  —  Figure  152  represents  a 
wooden  box  containing  what  is  equivalent  to  a  series  of  coils  of  German 
silver  wire,  whose  resistance  ranges  from  .01  ohm  to  100  ohms.      Each  of 
these  coils  is  connected  with  a  brass  stud  on  the  top  of  the  box. 

Three  switches,  A,  B,  and  C,  so  connect  the  coils  with  the  binding  screws 
a  and  b  that  a  current  can  be  sent  through  any  three  coils  at  the  same  time 
by  moving  the  switches  on  to  the  proper  studs.  The  resistance  in  ohms 


RESISTANCE   OF   CONDUCTORS.  179 

of  each  coil  is  marked  on  the  box  near  its  stud.     When  the  three  switches 

rest  upon  studs  marked  0,  the  current  meets  with  no  appreciable  resist- 

ance in  passing  through 

the  box,  but  any  desired 

resistance     within      the 

range  of  the  instrument 

can    be    introduced    by 

moving  the  switches  on 

to  the  studs,  the  sum  of 

whose  resistances  is  the 

resistance  required.  This 

instrument    is    called   a 

rheostat. 

Fig.  152. 

Experiment  137.  —  Measure  in  ohms  the  resistance  of  the  wire  on 
each  one  of  the  spools  used  above,  as  follows  :  —  Introduce  into  circuit 
(as  in  Figure  151)  a  galvanometer  and  the  spool  whose  resistance  is 
sought.  Note  the  deflection  in  degrees.  Then  remove  the  spool,  and 
introduce  the  rheostat  in  its  place.  Place  all  the  switches  on  the  zero 
studs.  The  deflection  of  the  galvanometer  needle  is  now  evidently 
greater  than  when  the  spool  was  in  circuit.  Move  the  switches,  throw- 
ing in  or  taking  out  resistance  (much  as  you  use  weights  in  weighing), 
until  the  deflection  becomes  the  same  as  the  deflection  was  when  the 
spool  was  in  circuit.  It  is  evident  that  the  sum  of  the  resistances,  as 
indicated  by  the  three  switches,  must  be  the  same  as  the  required 
resistance  of  the  wire  on  the  spool. 

In  the  same  manner,  measure  the  resistance  of  the  electro-magnets 
of  telegraph  sounders,  relays,  incandescent  lamps,  etc. 

The  method  of  measuring  resistance  given  above  is 
called  the  method  by  substitution  or  balancing.  The  results 
obtained  by  this  method  are  accurate  only  on  condition 
that  the  electro-motive  force  and  internal  resistance  of  the 
battery  remain  sensibly  constant  throughout  the  operation. 
This  rarely  happens,  so  that  the  results  obtained  can  be 
regarded  as  only  approximately  correct.  When  great 
accuracy  is  required,  it  is  necessary  that  some  means  of 
measuring  should  be  adopted  in  which  the  fluctuations  of 


180 


ELECTRICITY   AND   MAGNETISM. 


Fig.  153. 


the  battery  will  not  affect  the  results.  This  difficulty  is 
obviated  by  the  use  of  the  invaluable  instrument  called 
(from  the  name  of  its  inventor)  the  Wheatstone  bridge. 

156.  Wheatstone  Bridge.  —  Figure  153  represents  a  perspective 
f  ,  view  of  the  bridge  (as  modified 

1   f  V   T  -  /  bv  the  Author),  and  Figure  154 

represents  a  diagram  of  the  es- 
sential electrical  connections. 
The  battery  wires  are  connected 
with  the  bridge  at  the  binding 
screws,  BB'.  A  galvanometer  g 
is  connected  at  GG',  a  rheostat 
r  at  RR,  and  the  object  x,  whose  resistance  is  sought,  at  XX. 

On  closing  the  circuit  by  pressing  on  the  knob  T  the  current,  we  will  sup- 
pose, enters  at  B ;  on  reaching  the  point  A  it  divides,  one  part  flowing  via 

the  branch  AGB',  and  the  other 
via  the  branch  ADB'.  If  points  D 
and  G  in  the  two  branches  have 
different  potentials  and  a  con- 
nection is  made  between  them 
through  the  galvanometer,  g, 
by  pressing  on  the  knob  S,  there 
will  be  a  current  through  this 
bridge  wire  and  through  the 
.  galvanometer,  and  a  deflection 
of  the  needle  will  be  produced. 
But  if  the  points  D  and  G  have 
the  same  potential,  there  will 
be  no  cross  current  through  the 
bridge  wire  and  no  deflection. 
Now  it  can  be  demonstrated 
that  points  D  and  G  will  have 
the  same  potential  when  R  (the 
resistance)  of  AD  :  R  of  DB' : :  R  of  AG :  R  (the  unknown  resistance) 
of  GB'.  Between  A  and  D  and  A  and  G  there  are  three  coils  of  wire 
having  resistances  respectively  of  1,  10,  and  100  ohms.  One  or  more  of 
these  coils  are  introduced  into  the  circuit  by  removing  the  corresponding 
plugs  a,  b,  c,  d,  e,  and  f.  As  the  other  connections  between  A  and  D,  and 
A  and  G,  have  no  appreciable  resistance,  being  for  the  most  part  short 
brass  bars,  the  only  practical  resistance  between  these  points  is  that  intro- 


RESISTANCE   OF   CONDUCTORS.  181 

duced  at  will  through  the  coils.  Similarly  between  points  D  and  B',  the 
only  practical  resistance  is  that  introduced  at  will  through  the  rheostat, 
and  between  points  G  and  B'  the  resistance  is  the  resistance  (#)  sought. 

It  is  apparent,  then,  that  in  using  the  bridge  after  the  connections  are 
properly  made  through  the  several  instruments  and  certain  known  resist- 
ances are  introduced  between  A  and  D,  and  A  and  G,  we  have  simply  to 
regulate  the  resistance  through  the  rheostat  so  that  there  will  be  no  deflec- 
tion in  the  galvanometer;  then  we  are  sure  that  the  above  proportion  is 
true.  The  first  three  terms  of  the  proportion  being  known,  the  fourth 
term,  which  is  the  resistance  sought,  is  computable. 

In  using  the  instrument,  observe  the  following  directions.  (1)  Always 
close  the  circuit  at  T  before  closing  the  bridge  connections  at  S.  (2) 
Introduce  between  A  and  D,  and  A  and  G,  resistance  as  nearly  equal  to 
the  resistance  (x)  sought  as  practicable,  as  the  galvanometer  is  then  most 
sensitive.  If  you  have  no  conception  what  the  unknown  resistance  is,  it  is 
best  to  begin  by  using  high  resistances.  (3)  The  sensitiveness  of  the  gal- 
vanometer may  be  greatly  increased  by  placing  on  the  table  a  bar  magnet 
in  the  magnetic  meridian  with  its  north-seeking  pole  turned  toward  the 
north-seeking  pole  of  the  needle. 

Experiment  138.  —  Measure  the  resistances  of  the  several  spools 
of  wire  used  above,  —  electro-magnets,  electric  lamps,  etc.,  —  using 
the  bridge.  Place  the  switches  of  the  rheostat  on  the  zero  studs. 
Make  connections  as  in  the  description  above.  Then  close  the  circuit 
at  T,  and  afterward  the  bridge  at  S.  There  will  probably  be  a  deflec- 
tion in  the  galvanometer.  Regulate  the  resistance  through  the  rhe- 
ostat, throwing-  in  or  taking  out  resistance  according  as  one  or  the 
other  tends  to  reduce  the  deflection  (the  process  is  much  as  in  weigh- 
ing), until  there  is  no  deflection.  Then  compute  the  resistance  sought 
according  to  the  above  proportion.  Compare  the  results  with  those 
obtained  by  the  process  of  substitution. 

Experiment  139.  —  Measure  the  resistance  of  the  human  body. 
Let  some  person  grasp  in  his  dry  hands  two  metallic  handles,  such  as 
are  used  in  giving  shocks;  connect  the  handles  by  wires  at  XX. 
Introduce  100  ohms  between  A  and  G,  and  1  or  10  ohms  between 
A  and  D,  and  proceed  as  hitherto. 

The  cuticle,  or  dry  outer  skin  of  the  body,  offers  great  resistance. 
Let  the  same  person  wet  his  hands,  and  measure  the  resistance  again, 
and  ascertain  how  much  the  wetting  of  the  cuticle  reduces  the  resist- 
ance. Then  let  the  person  wet  his  hands  with  strong  salt  brine,  and 
once  more  measure  the  resistance. 


182  ELECTRICITY  AND   MAGNETISM. 


Section  IX. 

ELECTRO-MOTIVE  FORCE  OF  DIFFERENT  BATTERIES; 
OHM'S  LAW. 

157.  Electro-Motive    Force    of   Different  Batteries. 

—  If  a  galvanometer  is  introduced  into  a  circuit  with 
different  battery  cells,  e.g.  Bunsen,  Grenet,  Daniell,  etc., 
very  different  deflections  will  be  obtained,  showing  that  the 
different  cells  yield  currents  of  different  strength.  This 
may  be  due  in  some  measure  to  a  difference  in  their  inter- 
nal resistance,  but  it  is  chiefly  due  to  the  difference  in  their 
electro-motive  force.  We  learned  (page  161)  that  differ- 
ence of  electro-motive  force  is  due  to  the  difference  of  the 
chemical  action  on  the  two  plates  used,  and  this  depends 
largely  upon  the  nature  of  the  substances  used.  It  is  wholly 
independent  of  the  size  of  the  plates;  hence  the  electro- 
motive force  of  a  large  battery  cell  is  no  greater  than  that 
of  a  small  one  of  the  same  kind.  Consequently  any  dif- 
ference in  strength  of  current  yielded  by  battery  cells  of 
the  same  kind,  but  of  different  sizes,  is  due  wholly  to  a 
difference  in  their  internal  resistance. 

The  electro-motive  force  of  the  Bunsen,  Grenet,  and 
Daniell  cells  are  respectively  about  1.8,  2,  and  1  volts. 

In  consequence  of  polarization  of  the  plates,  the  electro-motive  force  of 
most  batteries  diminishes  more  or  less  rapidly  after  beginning  to  work. 
For  example,  the  current  of  the  Leclanche'  battery  weakens  so  rapidly  that 
it  can  be  used  only  in  cases  in  which  the  battery  is  required  to  work  only 
for  a  few  minutes  at  a  time,  such  as  for  ringing  annunciator  bells, 
telephony,  etc. 

158.  Ohm's  Law. —  The  strength  of  current  in  any  vol- 
taic circuit  varies  directly  as  the  electro-motive  force  and  in- 


ELECTRO-MOTIVE   FOKCE. —  OHM'S   LAW.  183 

versely  as  the  total  resistance  of  the  circuit.  Likewise,  the 
current  between  any  two  points  varies  as  the  difference  of 
potential  between  those  points,  and  inversely  as  the  resist- 
ance to  be  overcome.  This  law  is  usually  expressed  in 
the  form  of  the  mathematical  formula 

F  F 

C  =  T>  ;  whence  E  =  RC,  and  R  =  ^t 

in  which  C  represents  the  strength  of  current,  E  the  elec- 
tro-motive force,  and  R  the  entire  resistance.  The  above 

F 

fraction  — ,  when  the  external  resistance  is  considered  sepa- 
K 

rately  from  the  internal,  must  be  converted  thus ;  calling 
the  former  R,  and  the  latter  r,  the  expression  becomes 


R  +  r 

If  a  cell  has  E  =  1  volt,  and  r  =  1  ohm,  and  the  connecting 
wire  is  short  and  stout,  so  that  R  may  be  disregarded,  then 
the  current  has  a  value  of  one  ampere.  In  other  words,  an 
ampere  might  be  defined  as  the  strength  of  current  which 
an  electro-motive  force  of  one  volt  will  maintain  through 
a  resistance  of  one  ohm. 

EXERCISES. 

1.  What  E.M.F.  is  required  to  maintain  a  current  of  one  ampere 
through  a  resistance  of  one  ohm  ? 

2.  An  E.M.F.  of   10  volts  will  maintain  a  current  of   5  amperes 
through  what  resistance  ? 

3.  What  current  ought  an  E.M.F.  of  20  volts  to  maintain  through 
a  resistance  of  l\  ohms  ? 

4.  A  volt-meter  applied  each  side  of  an  electric  lamp  shows  a  dif- 
ference of  potential  of  40  volts;  what  current  flows  through  the  lamp, 
if  it  has  a  resistance  of  10  ohms  ? 

5.  The  resistance  between  two  points  in  a  circuit  is  10  ohms.     An 


184  ELECTllICITY    AND   MAGNETISM. 

ammeter  (an  instrument  which  measures  the  strength  of  a  current  in 
amperes)  shows  that  there  is  a  current  strength  in  the  circuit  of  0.5 
ampere  ;  what  is  the  difference  in  potential  between  the  points  ? 

6.  What  current  will  a  Bunsen  cell  furnish  when  r~  0.9  ohm  (about 
the  resistance  of  a  quart  cell),  E  =  1.8  volts,  and  R  =  0.01  ohm  (about 
the  resistance  of  3  ft,  of  No.  16  wire)? 


Section  X. 

DIVIDED   CIRCUITS  :    METHODS   OF   COMBINING   VOLTAIC 

CELLS. 

159.     Divided  Circuits  ;     Shunts. 

Experiment  140.  —  Make  a  divided  circuit  as  in  Figure  155  (using 
double  connectors  a  and  &).  Insert  a  galvanometer,  G,  in  one  branch 
and  a  rheostat,  R,  in  the  other.  The  current,  when 
it  reaches  a,  divides,  a  portion  traversing  one  branch 
through  the  galvanometer,  and  the  remainder  passes 
through  the  other  branch  and  the  rheostat.  Either 
branch  may  be  called  a  shunt  to  the  other.  Increase 
gradually  the  resistance  in  the  rheostat.  The  result  is 
that  it  throws  more  of  the  current  through  the  gal- 
vanometer, as  shown  by  the  increase  of  deflection. 

ITig.  155. 

In  a  divided  circuit  the  current  divides  between  the  paths 
inversely  as  their  resistances.  For  example,  if  the  resistance 
of  the  rheostat  above  is  4  ohms  and  the  resistance  in  the 
galvanometer  is  1  ohm,  then  four-fifths  of  the  current  will 
traverse  the  latter  and  one-fifth  the  former. 

Suppose  that  the  rheostat  and  galvanometer  are  removed 
from  the  shunts,  and  that  the  shunts  are  of  the  same  length, 
size,  and  kind  of  wire,  and  consequently  have  equal  resist- 
ances. Using  the  two  wires  instead  of  one  to  connect  a 


METHODS   OF   COMBINING    VOLTAIC   CELLS.  185 

and  b  is  equivalent  to  doubling  the  size  of  this  portion  of 
the  conductor ;  consequently  the  resistance  of  this  portion 
is  reduced  one-half. 

Generally,  the  joint  resistance  of  two  branches  of  a  circuit 
is  the  product  of  their  respective  resistances  divided  by  their 
mm.  (For  demonstration  of  this  law,  see  Gray's  Absolute 
Measurements  in  Electricity,  page  84.) 

16O.    Methods  of  Combining  Cells. 

Experiment  141.  —  Take  two  Bunsen  cells,  and  connect  the  two 
zinc  plates  by  a  wire.  Then  connect  each  of  the  carbon  plates  with 
a  galvanometer.  The  current  from  the  two  cells,  if  there  were  any, 
would  flow  in  opposite  directions.  But  you  find  that  there  is  either 
no  deflection  in  the  galvanometer,  or  at  most  a  very  small  one,  and 
this  shows  either  that  there  is  no  current  or  that  the  current  is  very 
weak.  The  reason  is  evident.  You  have  connected  two  carbons, 
which  have  theoretically  the  same  potential,  through  the  galvanome- 
ter; consequently  there  should  be  no  current  between  them.  The 
cells  are  said  to  be  connected  in  opposition. 

A  very  simple  way  of  showing  that  a  large  cell  has  no 
greater  electro-motive  force  than  a  small  one  is  to  connect 
two  such  cells  in  opposition  through  a  galvanometer,  or, 
what  answers  the  same  purpose,  raise  the  zinc  of  one  of 
two  cells  of  the  same  size,  connected  in  opposition,  nearly 
out  of  the  liquid.  The  absence  of  a  current  shows  that 
the  two  carbons  have  the  same  potential,  and  conse- 
quently their  electro-motive  force  is  the  same. 

A  number  of  cells  connected  in  such  a  manner  that  the 
currents  generated  by  all  have  the  same  direction  consti- 
tutes a  voltaic  battery. 

The  object  of  combining  cells  is  to  get  a  stronger  cur- 
rent than  one  cell  will  afford.  We  learn  from  Ohm's  law 
that  there  are  two,  and  only  two,  ways  of  increasing  the 
strength  of  a  current.  It  must  be  done  either  by  increasing 


186 


ELECTRICITY  AND   MAGNETISM. 


the  E.M.F.  or  by  decreasing  the  resistance.  So  we  com- 
bine cells  into  batteries,  either  to  secure 
greater  E.M.F.,  or  to  diminish  the  internal 
resistance.  Unfortunately,  both  purposes  can- 
not be  accomplished  by  the  same  method. 

161.  Batteries  of  Low  Internal  Resist- 
ance.—  Figure  156  represents  three  cells 
having  all  the  carbon  (c)  plates  electrically 
connected  with  one  another,  and  all  the 
zinc  (2)  plates  connected  with  one  another, 
and  the  triplet  carbons  are  connected  by  the 
leading-out  wires  through  a  galvanometer 
with  the  triplet  zincs. 

It  is  easy  to  see  that  through  the  battery 
the  circuit  is  divided  into  three  parts,  and 
consequently  the  conductivity  in  this  part  of 
rig.  156.       the  cjrcuit,  according  to  the  principle  stated 
in  §  159,  must  be  increased  threefold ;  in  other  words,  the 
internal  resistance  of  the  three  cells  is  one-third  of  that  of 
a  single  cell.     This  is  called  connecting  cells  "  abreast," 

or  "in  multiple  arc,"  and 
the  battery  is  called  a 
"  battery  of  low  internal 
resistance."  The  resistance 
of  the  battery  is  decreased 
as  many  times  as  there  are 
cells  connected  in  "arc," 
but  the  E.M.F.  is  that  of 
Fig'  157'  one  cell  only. 

162.  Batteries  of  High  Internal  Resistance  and 
Great  E.M.F.  —  Figure  157  represents  four  cells  having 
the  carbon  or  +  plate  of  one  connected  with  the  zinc  or 


I   I  1 1   I 


METHODS   OF   COMBINING   VOLTAIC   CELLS.  187 

-  plate  of  the  next,  and  the  +  plate  at  one  end  of  the 
series  connected  by  leading-out  wires  through  a  galva- 
nometer with  the  -plate  at  the  other  end  of  the  series. 
It  is  evident  that  the  current  in  this  series  traverses  the 
liquid  four  times,  which  is  equivalent  to  lengthening 
the  liquid  conductor  four  times,  and,  of  course,  increasing 
the  internal  resistance  fourfold.  But,  while  th'e  internal 
resistance  is  increased,  the  E.M.F.  of  the  battery  is  in- 
creased as  many  times  as  there  are  cells  in  series.  The 
gain  by  increasing  the  E.M.F.  more  than  offsets,  in  many 
cases  (always  when  the  internal  resistance  is  a  small 
part  of  the  whole  resistance  of  the  circuit),  the  loss 
occasioned  by  increased  resistance. 

163.    Best  Arrangement  of  Cells. 

Experiment  142.  —  Introduce  into  circuit  with  a  single  Bunsen 
cell  a  rheostat  and  a  galvanometer.  Throw  a  resistance  of  (say)  50 
ohms  into  the  circuit  by  means  of  the  rheostat.  Note  the  deflection. 
Then  add  another  cell,  in  series,  to  the  cell  already  in  use.  The  de- 
flection is  considerably  increased.  Other  cells  may  be  added  with 
similar  results. 

Experiment  143.  —  Connect  the  two  cells  abreast,  keeping  the 
same  resistance  in  the  rheostat.  The  deflection  is  only  a  very  little 
greater  than  that  caused  by  a  single  cell. 

Experiment  144.  —  Connect  a  single  cell  with  a  galvanometer1  of 
low  resistance,  so  that  the  whole  external  resistance  may  be  less  than 
the  resistance  of  the  single  cell.  Note  the  deflection.  Then  introduce 
another  cell  abreast.  The  deflection  is  considerably  increased. 

Experiment  145.  —  Connect  the  same  cells  in  series.  The  deflec- 
tion differs  but  little  from  that  produced  by  a  single  cell. 

Hence  (1)  ivhen  the  external  resistance  is  large,  connect 
cells  in  series  ;  (2)  when  the  external  is  less  than  the  internal 
resistance,  connect  cells  in  arc. 

1  The  galvanometers  furnished  by  the  author  have  a  resistance  of  about  one  ohm. 
The  internal  resistance  of  a  Bunsen  cell  can  easily  be  made  greater  than  this  if  the  cell 
is  filled  not  more  than  one-fifth  full  with  liquid. 


188  ELECTRICITY   AND   MAGNETISM. 

The  maximum  current  with  a  given  number  of  cells 
through  a  given  external  resistance  is  attained  when  the 
external  and  internal  resistances  are  most  nearly  equal. 

Caution:  —  Never  increase  the  external  resistance  for 
the  purpose  of  making  the  two  resistances  equal. 

EXERCISES. 

In  the  following  exercises,  whenever  a  Bunsen  cell  is  mentioned  it 
may  be  understood  to  be  a  quart  cell,  having  a  resistance  of  about  0.9 
ohm.  Its  E.M.F.  is  about  1.8  volt. 

1.  (a)  When  is  a  large  cell  considerably  better  than  a  small  one? 
(&)  When  does  the  size  of  the  cell  make  little  difference  in  the  current? 

2.  If  you  have  a  dozen  quart  cells,  how  can  you  make  them  equiva- 
lent to  one  3  gallon  cell  ? 

3.  If  a  battery  of  10  cells  has  an  E.M.F.  ten  times  greater  than 
that  of  a  single  cell,  why  will   not   the  battery  yield  a  current   ten 
times  as  strong? 

4.  (a)  The  internal  resistance  of  ten  cells,  connected  in  arc,  is  what 
part  of  that  of  a  single  cell  ?   (6)  If  the  cells  were  connected,  in  series, 
how  would  the  resistance  of  the  battery  compare  with  that  of  one  of 
its  cells?    (c)  How  would  the  E.M.F.  of  the  latter  battery  compare 
with  that  of  a  single  cell? 

5.  What   current  will   a  single  Bunsen   cell  furnish  through   an 
external  resistance  of  10  ohms? 

6.  What  current  will  8  Bunsen  cells,  in  series,  furnish  through  the 
same  resistance? 

SOLUTION  :  -^-  =      L8x8      =  0.83  +  ampere. 
B  +  r      10  +  0.9x8 

7.  What  current  will  8  Bunsen  cells,  in  arc,  furnish  through  the 
same  external  resistance? 

Tfl  10 

SOLUTION  :  = '- =  0.17  +  ampere. 

R  +  r      10 +(0.9 -=-8) 

8.  What  current  will  a  Bunsen  cell  furnish  through  an  external 
resistance  of  0.4  ohm? 

9.  What  current  will  a  battery  of  two  Bunsen  cells,  in  series,  fur- 
nish through  the  same  resistance  as  the  last? 

10.  What  current  will  two  cells,  in  arc,  furnish  through  the  same 
resistance  ? 


TRANSFORMATION   OF   ELECTRIC   ENERGY.  189 

Section  XI. 

TRANSFORMATION   OF  ELECTRIC   ENERGY  INTO   HEAT. 

164.    Transformation  Inside  and  Outside  a  Battery. 

Experiment  146.  —  Arrange  two  batteries,  each  consisting  of  two 
(Bunsen)  cells  connected  in  arc.  Use  thick  copper  wire  for  leading- 
out  wires.  Attach,  by  means  of  a  connector,  a  piece  of  platinum  wire 
about  1  inch  long  to  one  of  the  electrodes  of  one  of  the  batteries. 
Place  a  thermometer  in  the  dilute  acid  of  one  cell  of  each  of  the 
batteries.  Close  the  circuits  of  both  batteries  (one  through  the  plati- 
num wire)  at  the  same  moment.  Watch  for  changes  of  temperature 
in  the  liquids.  The  temperature  of  the  battery  which  is  not  in  circuit 
with  the  platinum  wire  rises  faster  than  the  other. 

That  portion  of  the  energy  of  an  electric  current  which 
is  not  transformed  into  heat,  or  other  kind  of  work,  in  other 
parts  of  the  circuit,  is  transformed  into  heat  in  the  battery. 

The  transformation  is  greatest  where  the  resistance  is 
greatest.  The  platinum  wire  being  small,  and  having  a 
relatively  large  specific  resistance,  offers  much  more  resist- 
ance to  the  current  than  the  copper  wire,  consequently  it 
becomes  much  hotter.  Much  of  the  electric  energy  being 
transformed  into  heat  in  the  platinum  wire,  there  is  less 
to  be  transformed  in  the  battery;  consequently  the  battery 
remains  comparatively  cool. 


Section  XII. 

MAGNETS   AND   MAGNETISM. 

165.   Law  of  Magnets.  —  Suspend  by  fine  threads  in  a 
horizontal  position  two  stout  darning-needles  which  have 


190  ELECTRICITY   AND   MAGNETISM. 

been  drawn  in  the  same  direction  (e.g.  from  eye  to  point) 
several  times  over  the  same  pole  (better  the  —pole)  of  a 
powerful  electro-magnet.  These  needles,  separated  a  few 
feet  from  each  other,  take  positions  parallel  with  each 
other,  and  both  lie  in  a  northerly  and  southerly  direction 
with  the  points  of  each  turned  in  the  same  direction. 

That  point  in  the  Arctic  zone  of  the  earth  toward  which 
magnetic  needles  point  is  called  the  north  magnetic  pole 
of  the  earth.  That  end  of  a  needle  which  points  toward 
the  north  magnetic  pole  of  the  earth  is  called  the  north- 
seeking,  marked,  or  +  pole  (inasmuch  as  this  is  the  end 
that  is  always  marked  for  the  purpose  of  distinguishing 
one  from  the  other).  That  end  of  the  needle  which 
points  southward  is  called  the  south-seeking,  unmarked, 
or  — pole. 

Experiment  147.  —  Bring  both  points  near  each  other ;  they  repel 
each  other.  Bring  both  eyes  near  each  other ;  they  likewise  repel 
each  other.  Bring  a  point  and  an  eye  near  each  other ;  they  attract 
each  other. 

Like  poles  of  magnets  repel,  unlike  poles  attract  one 
another. 

166.    Magnetic  Transparency  and  Induction. 

Experiment  148.  —  Interpose  a  piece  of  glass,  paper,  or  wood- 
shaving  between  the  two  magnets.  These  substances  are  not  them- 
selves perceptibly  affected  by  the  magnets,  nor  do  they  in  the  least 
affect  the  attraction  or  repulsion  between  the  two  magnets. 

Substances  that  are  not  susceptible  to  magnetism  are 
said  to  be  magnetically  transparent.  When  a  magnet 
causes  another  body,  in  contact  with  it  or  in  its  neighbor- 
hood, to  become  a  magnet,  it  is  said  to  induce  magnetism 
in  that  body;  i.e.  it  influences  it  to  be  like  itself.  As  attrac- 
tion, and  never  repulsion,  occurs  between  a  magnet  and 


MAGNETS   AND   MAGNETISM.  191 

an  unmagnetized  piece  of  iron  or  steel,  it  must  be  that  the 
magnetism  induced  in  the  latter  is  such  that  opposite  poles 
are  adjacent ;  that  is,  a  N  or  +  pole  induces  a  S  or  —  pole 
next  itself,  as  shown  in  Figure  158. 


Fig.  158. 

167.  Polarity. 

Experiment  149.  —  Strew  iron  filings  on  a  flat  surface,  and  lay 
a  bar-magnet  on  them.  On  raising  the  magnet,  it  is  found  that 
large  tufts  of  filings  cling  to  the  poles,  as  in  Figure  159, 
especially  to  the  edges ;  but  the  tufts  diminish  regularly  in 
size  from  either  pole  towards  the  centre,  where  none  are 
found. 

Magnetic  attraction  is  greatest  at  the  poles,  and 
diminishes  towards  the  center,  where  it  is  nothing, 
or  the  center  of  the  bar  is  neutral.  The  dual  char- 
acter of  the  magnet,  as  exhibited  in  its  opposite 
extremities,  is  called  polarity,  and  magnetism  is 
styled  &  polar  force.  If  a  magnet  is  broken,  each 
piece  becomes  a  magnet  with  two  poles  and  a 
neutral  line  of  its  own.  Fig.  159. 

168.  Coercive  Force.  —  It  is  more  difficult  to  magnet- 
ize steel  than  iron ;  on  the  other  hand,  it  is  difficult  to 
demagnetize  steel,  while  soft  iron  loses  nearly  all  its  mag- 
netism as  soon  as  it  is  removed  from  the  influence  of  the 
inducing  body.     The  quality  of  steel  by  which  it  at  first 
resists   the  power  of  magnets,  and  resists  the  escape  of 
magnetism  which  it  has  once  acquired,  is  called  coercive 
force.     The  harder  steel   is,  the  greater  is  its  coercive  force. 

Hence,  highly  tempered  steel  is  used  for  permanent  mag- 
nets.   Hardened  iron  possesses  considerable  coercive  force ; 


192  ELECTRICITY  AND   MAGNETISM. 

hence,  the  cores  of  electro-magnets  should  be  made  of  the 
softest  iron,  that  they  may  acquire  and  part  with  magnet- 
ism instantaneously. 

169.  Forms  of  Artificial  Magnets.  —  Artificial  mag- 
nets, including  permanent  magnets  and  electro-magnets, 
are  usually  made  in  the  shape  either  of  a  straight  bar,  or  of 
the  letter  U,  called  the  horseshoe,  according  to  the  use  made 
of  them.     If  we  wish,  as  in  the  experiments  already  de- 
scribed, to  use  but  a  single  pole,  it  is  desirable  to  have  the 
other  as  far   away  as  possible ;   then,  obviously,  the  bar 
magnet  is  most  convenient.     But  if  the  magnet  is  to  be 
used  for  lifting  or  holding  weights,  the  horseshoe  form  is 
far  better,  because  the  attraction  of  both  poles  is  conven- 
iently available,  and  because  their  combined  power  is  more 
than  twice  that  of  a  single  pole.     Magnets,  when  not  in 
use,  ought  always  to  be  protected  by  armatures  (A,  Fig. 
160)  of  soft  iron  ;  for,  notwithstanding  the  coercive  power 
of   steel,  they   slowly  part   with   their   magnetism.     But 
when  an  armature  is  used,  the  opposite  poles  of  the  mag- 
net and  armature  being  in  contact  with  one 
another,  i.e.  N  with  S,  they  serve  to  bind  one 
another's  magnetism.     Thin  bars  of  steel  can 
be    more    thoroughly   magnetized   than   thick 
ones.     Hence,  if  several  thin  bars  (Fig.  160) 
are  laid  side  by  side,  with  their  corresponding 
poles  turned  in  the   same  direction  and  then 
screwed  together,  a  very  powerful  magnet  is 
the  result.    This  is  called  a  compound  magnet. 

Fig.  160. 

1 7O.  Attraction    and  Repulsion   between  Currents : 
Laws  of  CurrentSo 

Experiment  150.  —  Figure  161  represents  a  portion  of  a  divided 
circuit.    The  lower  ends  of  the  wires  dip  at  the  lower  extremities  one- 


MAGNETS    AND   MAGNETISM. 


193 


sixteenth  of  an  inch  into  mercury,  and  they  are  so  suspended  that 
they  are  free  to  move  toward  or  from  each  other.  Send  a  current  of 
a  battery  of  two  or  three  Bunsen  cells,  in  arc,  through  this  divided 
circuit.  The  two  portions  of  the  current  travel  in  the  same  direction 
and  parallel  with  each  other,  and  the  two  wires  at  the  lower  extremi- 
ties move  toward  each  other,  showing  an  attraction. 

Experiment  151.  —  Make  the  connections  (Fig.  162)  so  that  the 
current  will  go  down  one  wire  and  up  the  other.  They  repel  each 
other. 


\ 

j 

\l 

\ 

\ 

i 

um 

^XJ" 

f       flf! 

m 

* 

b 

» 

Fig.  161.                  Fig.  162. 

Fig.  163. 


Experiment  152.  —  Send  a  current  through  the  spiral  wire  repre- 
sented in  Figure  163.  Here  the  current  flows  nearly  parallel  with 
itself,  and  the  attraction  causes  the  coil  to  contract  and  to  be  lifted 
out  of  the  cup  of  mercury  below.  But  the  instant  it  leaves  the  mer- 
cury the  circuit  is  broken,  the  current  and  attraction  cease,  and  the 
wire  dips  into  the  mercury  again.  Thus  rapid  vibratory  motion  of 
the  coil  is  produced. 

First  Law  of  Currents.  —  Parallel  currents  in  the  same 
direction  attract  one  another ;  parallel  currents  in  opposite 
directions  repel  one  another. 

Experiment  153.  —  Figure  164  represents  a  small  battery  floating 
on  water.  The  wire  of  the  battery  is  wound  into  a  horizontal  coil.  In 
a  few  minutes  after  the  battery  is  floated  it  will  take  a  position  so 
that  its  coil  will  point  north  and  south,  like  a  magnetic  needle. 


194 


ELECTRICITY  AND   MAGNETISM. 


Place  the  wire  of  another  battery  over  and  parallel  with  the  coil,  so 
that  the  two  currents  will  flow  in  planes  at  right  angles  with  each 
other.     The  coil  is  deflected  like  a  magnetic  needle.     A  careful  exami- 
nation  will    disclose 
the  fact  that  not  only 
have  the    planes    in 
which    the   two   cur- 
rents   flow     become 
parallel,  but  that  the 
current   in    the   half 
of    the    coil    (where 
Fig'  164>  the   influence  due  to 

proximity  is  greatest)  flows  in  the  same  direction  that  the  current  above 
it  flows. 

Reverse  the  direction  of  the  current  above  and  the  deflection  is 
reversed. 

Second  Law  of  Currents.  —  Angular  currents  tend  to 
become  parallel  and  flow  in  the  same  direction. 

Experiment  154.  —  Remove  the  primary  coil  from  the  secondary 
coil  (Fig.  169),  send  a  current  through  the  former,  and  hold  one  of  its 

ends  near  to  one  end  of  the  coil  of 
the  floating  battery,  as  in  Figure 
165,  in  such  a  manner  that  the  cur- 
rent will  flow  in  the  same  direction 
in  the  ends  presented  to  each  other. 
The  coils  attract  one  another  like 
two  magnets  in  accordance  with  the 

First  Law  of  Currents.    Present  the 
Fig.  165.  same  end  of  the  coil  to  the  o^er 

end  of  the  floating  battery  coil.     Now  the  currents  in  the  two  ends 
flow  in  opposite  directions,  and  the  coils  repel  each  other. 

Experiment  155.  —  Observe  that  at  one  end  of  the  floating  battery 
coil  the  current  revolves  in  the  direction  that  the  hands  of  a  watch 
move,  and  at  the  opposite  end  it  revolves  in  a  direction  contrary  to 
the  movement  of  the  hands  of  a  watch.  Bring  the  north  pole  of  a 
bar-magnet  near  that  end  of  the  coil  where  the  motion  of  the  current 
corresponds  to  the  movement  of  the  hands  of  a  watch.  They  attract 
one  another;  but  if  the  same  end  of  the  coil  is  approached  by  the 
south  pole  of  the  magnet,  repulsion  follows. 


MAGNETS   AND   MAGNETISM.  195 

Hence,  that  is  the  south  pole  of  a  helix  where  the  current  <Jorre- 

^~x 

spends  to  the  motion  of  the  hands  of  a  watch,  S,  and  that  is  the  north 

pole  where  the  current  is  in  the  reverse  direction,  N.  But  the  impor- 
tant lesson  derived  from  these  latter  experiments  is,  that  coils  through 
which  currents  are  flowing  behave  toward  one  another,  or  toward  a  mag- 
net, in  many  respects  as  if  they  were  magnets. 

171.  Ampere's  Theory  of  the  Magnet.  —  Facts  like 
those  which  we  have  just  studied  led  Ampere  to  devise  a 
theory  for  the  explanation  of  magnetism.  Little  credence 
is  given  to  this  theory  by  electricians  ;  nevertheless  a  slight 
acquaintance  with  it  is  of  great  service  to  the  beginner  in 
aiding  him  to  picture  to  himself  how  certain  phenomena 
occur.  Ampere  was  led  to  suppose  that  something  like  an 
infinite  number  of  currents  invests  at  all  times  every  piece 
of  steel,  iron,  and  other  magnetizable  substance.  That  in 
a  magnetizable  bar  of  steel  or  iron  these  currents  are  all 
parallel  with  one  another,  and  we  have  the  combined 
effects  (i.e.  of  attraction  or  repulsion)  of  all  the  currents. 
When  a  magnet,  having  all  its  currents  parallel,  is  brought 
near  to  an  unmagnetized  piece  of  iron  or  steel  in  which 
the.  currents  have  no  common  direction,  the  former  in- 
duces magnetism  in  the  latter,  i.e.  it  causes  the  currents 
of  the  latter  to  become  pcirallel  with  its  own,  in  accord- 
ance with  the  Second  Law  of  Currents.  For  convenience 
we  may  call  the  hypothetical  currents  Amperian  eurrnits. 


N 


Fig.  166. 

This  ingenious  theory  will  enable  us  to  understand  how 
the  core  of  the  electro-magnet  is  magnetized.  The  real 
currents  circulating  in  the  wire  outside  cause  the  Amp^r- 


196 


ELECTKICITY   AND   MAGNETISM. 


ian  currents  to  become  parallel  with  them,  and  as  both  flow 
in  the  same  direction  as  represented  in  Figure  166,  we 
have,  in  the  electro-magnet,  the  combined  effect  of  both 
sets  of  currents. 

1 72.  Lines  of  Magnetic  Force  ;   Magnetic  Field. 

Experiment  156.  —  Sup- 
port a  small  pane  of  window 
glass  on  a  table,  by  placing 
under  the  glass  near  its 
angles  four  slices  of  cork 
about  one-eighth  of  an 
inch  thick.  Beneath  the 
center  of  the  glass  on  the 
table  place  a  circular  disk 
of  magnetized  steel.  Sift 
iron  turnings  upon  the 
upper  face  of  the  glass 
through  a  fine  wire  sieve. 
Gently  tap  the  glass  at 
convenient  points  with  the 
end  of  a  lead-pencil.  The 
filings  arrange  themselves 
in  lines  radiating  from 
either  pole,  and  form  grace- 
ful curves  from  pole  to  pole, 
as  represented  in  Figure 
166a.  These  represent  what  are  called  lines  of  magnetic  force.  They 
represent  the  results  of  the  combined  action  of  the  two  poles. 

A  magnet  seems  to  be  surrounded  by  an  atmosphere  of  magnetic 
influence  called  the  magnetic  field.  A  body  brought  within  the  limit 
of  its  influence  is  said  to  be  within  the  field  of  the  magnet. 

173.  The  Earth  is  a  Magnet. — A  dipping-needle  is  so 
supported  that  it  can  revolve  in  a  vertical  plane.     Indiffer- 
ent equilibrium  is  first  established  in  the  steel  needle,  so 
that  if  placed  in  a  horizontal  (or  any  other)  position  it  will 
rest  in  that  position.     Then  it   is   strongly   magnetized. 


Fig.  166a. 


MAGNETS    AND   MAGNETISM.  197 

Afterward  it  will  take  the  horizontal  position  only  at  the 
magnetic  equator  of  the  earth. 

Experiment    157.  —  Place  a  dipping-needle  over  the  +  pole  of  a 
bar-magnet  (Fig.  167).      The  needle  takes  a  vertical  position  with 
its   —pole   down.      Slide   the    supporting  stand   along  the    bar;  the 
—  pole  gradually  rises 
until    it    reaches    the 
middle    of    the    bar, 
where  it  becomes  hori- 
zontal. Continue  mov- 
ing the  stand  toward 
the  —  pole  of  the  bar  ; 

after  passing  the  middle  of  the  bar  the  +  pole  begins  to  dip,  and  the 
dip  increases  until  the  needle  reaches  the  end  of  the  bar,  when  the 
needle  is  again  vertical  with  its  +  pole  down. 

If  the  same  needle  is  carried  northward  or  southward  along  the 
earth's  surface,  it  will  dip  in  the  same  way  as  it  approaches  the  polar 
regions,  and  be  horizontal  only  at  or  near  the  equator. 

Experiment  158.  —  Suspend  a  small  magnetized  cambric  needle  by 
a  fine  thread  at  its  center  and  carry  it  around  the  disk  (Fig.  166).  The 
needle  passes  through  all  the  phases  stated  above,  so  that  we  may 
fancy  the  disk  to  be  the  earth,  and  study  therefrom,  in  a  general  way, 
the  changes  that  the  needle  undergoes,  as  it  is  carried  around  the 
earth  in  a  northerly  or  southerly  direction. 

1 74.  Magnetic  Poles  of  the  Earth.  —  Those  points  on 
the  earth's  surface  where  the  dipping-needle  stands  vertical 
are  the  magnetic  poles  of  the  earth.  A  point  was  found  a 
little  northwest  of  Hudson's  Ba^,  in  latitude  70°  5'  N.,  and 
longitude  96°  45'  W.,  by  Sir  James  Ross,  in  the  year  1832, 
where  the  dipping-needle  lacked  only  one-sixtieth  of  a  de- 
gree of  being  vertical.  The  same  voyager  subsequently 
reached  a  point  in  Victoria  Land  where  the  needle  with  its 
poles  reversed  lacked  only  1°  20'  of  being  vertical. 

The  magnetic  poles  are  not,  however,  fixed  objects  that 
can  be  located  like  an  island  or  cape,  but  are  constantly 


198  ELECTRICITY   AND   MAGNETISM. 

changing.  They  appear  to  swing,  somewhat  like  a  pen- 
dulum, in  an  easterly  and  westerly  direction,  each  swing 
requiring  centuries  to  complete  it.  The  north  magnetic 
pole  is  now  on  its  westerly  swing. 

175.  Variation    of   the   Needle. — Inasmuch    as   the 
magnetic  poles  of  the  earth    do   not   coincide   with  the 
geographical  poles,  it    follows  that   in   most   places   the 
needle  does  not  point  due  north  and  south.     The  angle 
which  the  needle  makes  with  the  geographical  meridian 
is  known  as  the  angle  of  declination.     This  angle  differs 
at  different  places. 

176.  Inclination  or  Dip  of  the  Needle.  —  The  angle 
that   a   dipping-needle    makes   with   a   horizontal   line    is 
called   its  inclination  or  dip.     A  line   drawn  around  the 
earth   connecting   those    places   where   there   is    no    dip 
would  represent  the  magnetic  equator. 

Experiment  159.  —  Place  the  dipping-needle  on  a  horizontal  surface, 
apart  from  any  iron  (such  as  nails,  etc.),  and  so  that  the  plane  of  rota- 
tion of  the  needle  will  be  in  the  magnetic  meridian,  and  ascertain 
from  the  divided  arc  (approximately,  at  least)  the  dip  at  the  place 
where  you  live. 

EXERCISES. 

1.  Stretch  a  string  between  two  pins  stuck  in  a  table,  so  that  it  will 
lie  in  the  geographical  meridian,  i.e.  in  the  direction  of  the  North  Star. 
On  this  string  set  the  stand  holding  a  magnetic  needle  about  6  inches 
long.     Determine  whether  there  is  any  magnetic  declination  at  the 
place  where  you  are,  and,  if  so,  in  what  direction  it  is. 

2.  What  is  the  declination  and  dip  at  your  place  of  residence  ? 
Let  A  (Fig.  168)  represent  a  magnetic  pole  and  B  the  North  Star. 

It  will  be  seen  that  there  is  a  position  in  which  the  needle  will  point 
due  north.  A  line  passing  around  the  earth  through  the  two  magnetic 


CURRENT   AND   MAGNETIC   ELECTRIC   INDUCTION.      199 


poles,  connecting  those  places  where  the  needle  points  due  north,  is 
called  a  line  of  no  variation. 

3.  Take  a  map  of  the  United  States 
and  draw  on  it  a  pencil  line,  starting  at  a 
point  on  the  Atlantic  coast  where  the  two 
Carolinas  meet ;  continue  it  a  little  west  of 
Pittsburg,  Pa.,  and  through  lakes  Erie  and 
Huron,  and  this  line  will  represent  very  rig*  168> 

nearly  the  line  of  no  variation  at  the  present  time.  It  is  slowly 
moving  westward.  At  places  in  the  United  States  east  of  this  line 
the  +  pole  of  the  needle  points  west  of  north,  e.g.  the  New  England 
States  and  New  York ;  but  most  of  the  States  lie  west  of  this  line,  so 
in  them  the  needle  points  east  of  north.  At  Harvard  University,  in 
Cambridge,  Mass.,  in  1887,  the  declination  was  11.87°  W.  of  N. ;  in 
1872  it  was  0.7°.  In  1880  the  declination  at  Halifax,  N.S.,  was  20.3° 
W.  of  N. ;  at  San  Francisco  it  was  16.52°  E.  of  N. 


Section  XIII. 


CURRENT  AND   MAGNETIC   ELECTRIC    INDUCTION. 

177.  Description  of  Apparatus. —  A  (Fig.  169)  is  a  short  coil 
of  coarse  wire  (i.e.  the  wire  which 
it  contains  is  comparatively  short), 
and  has,  of  course,  little  resistance. 
B  is  a  long  coil  of  fine  wire  having 
high  resistance.  Coil  A  is  in  circuit 
with  two  Bunsen  cells  in  arc.  This 
circuit  we  call  the  primary  circuit, 
the  current  in  this  circuit  the  pri- 
mary or  inducing  current,  and  the 
coil  the  primary  coil.  Another  cir- 
cuit, having  in  it  no  battery  or 
other  means  of  generating  a  current, 
contains  coil  B  and  a  galvanoscope 
with  an  astatic  needle.  This  circuit 
is  called  the  secondary  circuit,  the 


200 


ELECTKICITY   AND   MAGNETISM. 


coil  the  secondary  coil,  and  the  currents  which  circulate  through  this  cir- 
cuit are  called  secondary  or  induced  currents. 

Experiment  160.  —  After  all  the  connections  are  made,  arid  a 
current  is  established  in  the  primary  circuit,  and  the  galvanoscope 
needle  is  brought  to  zero,  lower  the  primary  coil  quickly  into  the 
secondary  coil,  watching  at  the  same  time  the  needle  of  the  galvano- 
scope to  see  whether  it  moves,  and,  if  so,  in  what  direction.  Simul- 
taneously with  this  movement  is  a  movement  of  the  needle,  showing 
that  a  current  must  have  passed  through  the  secondary  circuit.  Let 
the  primary  coil  rest  within  the  secondary,  until  the  needle  comes  to 
rest.  After  a  few  vibrations  the  needle  settles  at  zero,  showing  that 
the  secondary  current  was  a  temporary  one.  Now,  watching  the 
needle,  quickly  pull  the  primary  coil  out;  another  deflection  in  an 
opposite  direction  occurs,  showing  that  a  current  in  an  opposite  direc- 
tion is  caused  by  withdrawing  the  coil.  Just  how  the  necessary  con- 
dition {i.e.  E.M.F.)  for  an  electric  current  is  brought  about  we  do  not 
know;  but  we  do  know  that  it  is  done  under  the  influence  of  the 
primary  current  (hence  the  process  is  called  induction)  and  at  the  ex- 
pense of  mechanical  energy. 


Fig.  17O. 

Experiment  161.  —  Place  the  primary  coil  within  the  secondary. 
Open  the  primary  wire  at  f  some  point  and  then  close  the  circuit 
(Fig.  170)  by  bringing  in  contact  the  extremities  of  the  wires.  A 
deflection  is  produced.  As  soon  as  the  needle  becomes  quiet,  break 
the  circuit  by  separating  the  wires ;  a  deflection  in  the  opposite  direc- 
tion occurs. 

On  introducing  the  primary  coil  into  the  secondary,  and  on  closing 


CURRENT   AND  MAGNETIC   ELECTRIC   INDUCTION.        201 

the  primary  circuit,  currents  are  induced  in  the  reverse  direction  in 
the  secondary  circuit  that  the  primary  current  has ;  on  the  withdrawal 
of  the  primary  coil,  or  on  breaking  the  primary  circuit,  the  induced 
current  generated  is  in  the  same  direction  as  of  that  of  the  primary 
current. 

Experiment  162.  —  Introduce  the  bundle,  D  (Fig.  169),  of  soft 
iron  wires,  called  the  core,  into  the  primary  coil,  and  make  and  break 
the  primary  circuit  as  before.  The  deflections  are  now  very  much 
increased. 

Experiment  163.  —  Substitute  a  person  for  the  galvanometer  in  the 
secondary  circuit,  the  person  grasping  some  metallic  handles  made  for 
the  purpose  and  used  as  electrodes.  The  person  experiences  at  the 
instant  of  making  and  breaking  a  peculiar  sensation  in  his  wrists  and 
arms,  called  a  shock. 

Experiment  164.  —  Introduce  into  the  primary  circuit  the  auto- 
matic inake-and-break  piece  C  (Fig.  169).  Remove  the  core  from  the 
primary  coil.  Let  a  person  grasp 
the  electrodes  of  the  secondary 
circuit.  This  person  experiences 
a  series  of  shocks  which  seem  to 
him  almost,  if  not  quite,  contin- 
uous. These  shocks  can  be  in- 
tensified to  suit  the  pleasure  of 
the  person  who  is  receiving  them, 
by  gradually  lowering  the  core 
into  the  primary  coil.  But  no 
temptation  to  fun  should*  lead 
the  experimenter  to  be  so  cruel 
as  to  drop  the  core  into  the  coil 
suddenly.  Fis-  171- 

Experiment  165.  —  Reflecting  that  you  have  found  hitherto,  a  coil 
of  wire  having  a  current  passing  through  it  acting  as  a  magnet,  you 
have  now  an  opportunity  to  try  the  converse,  i.e.  to  see  whether  a 
magnet  may  not  take  the  place  of  a  current-bearing  coil.  Introduce 
suddenly  a  bar-magnet  (Fig.  171)  into  the  secondary  coil,  as  in  Ex- 
periment 160.  A  deflection  is  produced ;  withdraw  it  and  an  opposite 
deflection  occurs. 


202  ELECTRICITY   AND   MAGNETISM. 

Laws  of  Induced  Currents :    The   general  laws  of  in- 
duced currents  are  summed  up  in  the  following  table  :  — 


INDUCTOR. 

INVERSE  INDUCED 
CURRENT. 

DIRECT  INDUCED 
CURRENT. 

A  magnet    .    .    . 

Approaching. 

Receding. 

A  current    .    .    . 

(  Approaching. 
)  Beginning. 
(  Increasingin  strength. 

{Receding. 
Stopping. 
Diminishing  in  strength. 

178.  Extra    Currents.  —  Pupils,  while  handling   the 
naked  electrodes  of  a  battery  having  an  electro-magnet  or 
other  coil  in  the  circuit,  at  the  instant  of  dropping  or  tak- 
ing hold   of   the    electrodes   frequently  experience  slight 
shocks.     This  is  due  to  what  are  called  extra  currents  in- 
duced in  the  battery  circuit  itself  at  the  instants  of  making 
and  breaking.     As  the  battery  current  advances  or  retires 
through  the  wire,  each  convolution  of  wire  acts  inductively 
upon  the  neighboring  convolutions,  in  a  manner  similar  to 
that  of  the  primary  coil  upon  the  secondary.     The  sparks 
invariably  attending  the  touching  and  separating  of  elec- 
trodes, e.g.    those   seen    at   the   nmke-and-break   piece   C 
(Fig.  169),  are  produced  by  extra  currents. 

1 79.  Ruhmkorff ' s  Induction  Coil.  —  Figure  172  represents,  in 
diagram,  an  ideal  induction  coil.     A  A  is  the  core  around  which  is  wound 
the  primary  wire.     Outside   of   the   whole   is   the   secondary  coil.     The 
directions  of  the  several  currents  are  indicated  by  arrows  at  the  instant  the 
primary  circuit  is  closed  at  6  in  the  automatic  piece  cd.     The  condenser 
B  B  was  the  important  addition  made  by  Ruhmkorff. 

It  consists  of  two  sets  of  layers  of  tin-foil  separated  by  paraffine  paper ; 
the  layers  are  connected  alternately  with  one  and  the  other  pole  of  the 
battery,  as  the  figure  shows,  so  that  they  serve  as  a  sort  of  expansion  of 
the  primary  wire.  When  the  circuit  is  broken,  the  extra  current  would 


CURRENT    AND   MAGNETIC    ELECTRIC    INDUCTION.       203 


jump  across  at  b,  and  would  vaporize  the  points  of  contact,  and  form  a 
bridge  with  the  vapor  of  metal  that  would  prolong  the  time  of  breaking. 
But,  when  the  condenser  is  attached,  the  extra  current  finds  an  escape  into 


Fig.    173. 

it  easier  than  to  jump  across  at  b,  so  the  vaporizing  of  the  contact  is 
avoided,  and  the  time  of  breaking  being  much  shortened,  the  secondary 
current  is  much  more  intense. 

Experiment  166.  —  Connect 
a  -battery  of  two  Bunsen  cells, 
in  arc,  with  a  Ruhmkorff  coil 
(Fig.  173) .  Bring  the  electrodes 
of  the  secondary  coil  within 
one-fourth  of  an  inch  to  one 
inch  of  each  other,  according  to 
the  capacity  of  the  instrument. 
A  series  of  sparks  in  rapid  suc- 
cession pass  from  pole  to  pole. 

Experiment  167.  —  Intro- 
duce a  Geissler  tube,  A,  into  the 
secondary  circuit.  These  tubes 

contain  highly  rarefied  gases  of  different  kinds.  Platinum  wires 
are  sealed  into  the  glass  at  each  end  to  conduct  the  electric  cur- 


204  ELECTKICITY    AND   MAGNETISM. 

rent  through  the  glass.  The  sparks  become  diffused  in  these  tubes 
so  as  to  illuminate  the  entire  tubes  with  an  almost  continuous  glow. 
Observe  that  the  electrodes  are  separated  from  each  other  much 
more  widely  than  would  be  admissible  in  air  of  ordinary  density, 
showing  that  rarefied  gases  offer  less  resistance  than  dense  gases. 
Gases  have  been  so  highly  rarefied,  however,  that  an  electric  cur- 
rent would  not  pass.  This  shows  that  a  material  conductor  and 
one  of  sufficient  density  is  absolutely  necessary  for  the  passage  of 
a  current. 

180.  Electric  Motor. 

Experiment  168.  —  This  experiment  will  require  two  separate  bat- 
teries. Join  one  battery  to  a  small  Ruhmkorff  coil,  and  connect  its 
secondary  coil  with  the  apparatus  represented  in  Figure  174,  intro- 
ducing the  wires  at  the  binding  screws, 
c  and  d.  Join  the  wires  of  the  other 
battery  with  the  same  instrument,  in- 
serting the  wires  at  the  binding  screws, 
a  and  b.  The  first  battery  in  conjunc- 
tion with  the  coil  causes  induced  cur- 
rents to  enter  this  instrument  and  pass 
through  the  Geissler  tube,  A.  The 
other  battery  causes  the  tube  to  rotate. 
In  a  darkened  room  the  appearance  is 
that  of  a  luminous  wheel  of  great 
beauty  having  many  spokes.  Various 
Fig.  174.  optical  illusions  attend  the  experi- 

ment, which  make  it  very  attractive. 

The  instrument  used  is  one  form  of  an  electric  motor.  An  electric 
motor  is  a  device  for  transforming  the  energy  of  an  electric  current 
into  mechanical  energy,  i.e.  into  motive  power.  It  is  usually  accom- 
plished through  the  use  of  electro-magnets,  and  hence  a  motor  is 
frequently  called  an  electro-magnetic  engine.  Electric  motors  of  great 
power  have  been  constructed,  and  are  successfully  used  for  propelling 
railway  cars,  etc. 

181.  Characteristics  of  Induced  Currents.  —  The  student 
cannot  have  failed  to  observe  that  induced  electricity  has  a  power  for 
penetrating  a  non-conductor  far   superior  to  that   of  primary  currents. 


DYNAMO-ELECTRIC   MACHINES.  205 

The  former  can  penetrate  the  air  passing  through  it  from  electrode 
to  electrode,  at  distances  varying  from  one-hundredth  of  an  inch  to 
three  feet  in  the  largest  induction  coils.  They  can  perforate  cardboard, 
panes  of  glass,  and  produce  various  other  mechanical  effects.  They  may 
be  so  intense  as  to  produce  instantaneous  death.  On  the  other  hand,  it 
would  require  the  E.M.F.  of  several  thousand  voltaic  cells  connected,  in 
series,  to  furnish  sufficient  power  to  penetrate  the  air  so  as  to  maintain 
a  current  when  the  electrodes  are  separated  only  one-hundredth  of  au 
inch. 


Section  XIV. 

,. 

DYNAMO-ELECTRIC^  MACHINES. 

182.  A  Simple   Dynamo  and  the  Gramme  Dynamo. 

Experiment  169.  —  Take  the  secondary  coil  of  the  induction  coil 
apparatus  (Fig.  169),  place  within  it  the  core  of  iron  wires.  Introduce 
into  circuit  with  this  coil  a  galvanoscope  with  an  astatic  needle.  Take 
a  powerful  compound  horseshoe ;  suspend  it  in  a  vertical  position 
with  the  poles  downward.  Move  the  coil  back  and  forth  under  and 
near  to  the  magnet,  so  that  the  core  will  come  alternately  under  each 
pole.  Deflections  alternating  in  direction  show  the  production  of 
induced  currents. 

The  student  should  look  thoughtfully  at  this  contrivance,  be- 
cause he  has  before  him  a  dynamo-electric  machine  in  its  simplicity. 
It  consists,  like  all  the  more  complicated  machines,  of  these  two 
essential  parts,  viz.  (usually)  a  long  coil  containing  an  iron  core, 
constituting  an  armature,  and  a  powerful  magnet  (either  a  perma- 
nent steel  magnet,  or,  more  frequently,  because  more  powerful, 
an  electro-magnet)  called  the  field  magnet.  The  method  by  which 
currents  are  generated  in  this  contrivance  and  in  all  dynamos  is  the 
same,  viz.  by  the  movement  of  an  armature  within  the  field  of  an  electro- 
magnet. 


206 


ELECTRICITY   AND   MAGNETISM. 


Much  more  than  the  above  it  is  not  important  that  the  general  student 
should  know.  Matters  of  detail  differ  widely  in  different  machines,  and 
the  student  is  not  supposed  to  be  especially  interested  in  any  particular 
machine.  To  give  a  full  and  intelligible  description  of  any  machine  in  a 
single  page  is  not  an  easy  matter.  For  the  benefit  of  the  more  ambitious 
students,  we  submit  the  following  condensed  description  of  the  Gramme 
dynamo.  Its  armature,  ns  (Fig.  175),  con- 
sists of  a  ring  composed  of  a  bundle  of 
soft  iron  wires  (better  shown  in  Figure 


Fig.  175. 


Fig.  176. 


177,  Plate  III.)  surrounded  by  what  is  virtually  an  endless  coil  of  wire. 
The  wire,  however,  is  wound  in  sections  separated  by  suitable  partitions, 
and  the  wire  of  each  section  carried  to  and  connected  electrically  with  a 
copper  plate  on  the  axle  mm.  The  several  copper  plates  (as  many  as 
there  are  sections)  are  insulated  from  one  another.  (To  enable  the 
pupil  better  to  understand  the  method  of  winding,  making  connections, 
etc.,  the  author  has  prepared  a  model  (Fig.  176)  of  this  machine,  which 
will  furnish  at  a  glance  information  respecting  the  method  of  winding, 
making  connections,  etc.,  which  no  book  can  do.)  A  horseshoe  magnet 
NS  (only  a  portion  of  which  is  shown  in  the  cut)  is  so  placed  that  one- 
half  of  the  ring  is  under  the  influence  of  the  N-pole,  and  the  other  half 
under  that  of  the  S-pole.  Suppose  the  ring  to  rotate  in  the  direction  of 
the  arrow;  then  every  point  of  the  iron  core,  as  it  comes  opposite  a 
given  point  of  the  magnet,  will  successively  become  a  pole  of  opposite 
name,  while  the  points  i  and  i'  are  the  neutral  points. 


Plate  III. 


PigT.  177. 


DYNAMO-ELECTRIC   MACHINES.  207 

If  we  imagine  the  core  to  be  divided  at  the  points  n  and  s,  we  have 
two  semicircular  magnets  whose  north  poles  and  whose  south  poles  re- 
spectively face  one  another.  In  the  two  mutually  facing  poles  on  either 
side,  the  Amperian  currents  must  be  in  opposite  directions.  Now  an 
attentive  study  of  this  ideal  diagram,  in  the  light  of  what  you  have 
previously  learned  respecting  the  generation  of  induced  currents,  will 
enable  you  to  see  that  as  the  ring  armature  rotates,  the  corresponding 
advance  of  the  induced  poles  of  the  ring  will  induce  currents  in  the  wire 
in  such  a  manner  that  all  the  coils  which  at  any  given  moment  are  in  the 
semicircle  next  one  of  the  magnet  poles  (say  the  North)  are  traversed 
by  a  current  in  one  direction.  Similarly,  the  semicircle  formed  by  the 
coils  immediately  approaching,  or  immediately  receding  from  the  South 
pole  are  at  thfe  same  time  traversed  by  a  current  in  the  opposite  direction. 
The  result  is  that  currents  in  the  lower  half  tend  toward  the  point  m  on 
the  axis,  and  in  the  upper  half  from  point  m'.  So  long  as  the  leading-out 
wires  from  these  points  are  open,  these  currents  have  no  outlet,  and  conse- 
quently oppose  and  neutralize  one  another.  But  if  the  points  m  and  m' 
are  connected  by  a  wire  L,  we  shall  have  a  constant  and  non-alternating  cur- 
rent flowing  through  the  wire  from  m  to  m'.  The  contact  at  these  points 
is  made  by  means  of  brushes  of  thick  wire.  These  press  on  the  contact 
pieces,  and  make  practically  a  constant  connection  with  the  two  halves  of 
the  circuit. 

Inasmuch  as  an  electro-magnet  may  be  made  a  much  more  powerful 
magnet  than  a  permanent  magnet,  it  is  now  extensively  used  as  the  induc- 
ing or  the  so-called  field  magnet.  Such  a  machine  is  called  a  dynamo-elec- 
trical machine,  or  often  more  briefly  a  dynamo.  Figure  178,  Plate  III., 
represents  such  a  machine.  EE  is  the  stationary  field  magnet,  A,  the 
moving  armature,  and  N  and  S  large  pole-pieces  brought  as  near  as  prac- 
ticable to  the  armature  and  partially  encircling  it.  When  the  machine 
is  at  rest,  there  are  no  currents ;  but  when  the  armature  is  in  motion,  the 
residual  magnetism  (a  small  portion  of  which  is  always  retained  by  soft  iron 
after  it  has  been  magnetized)  induces  at  first  a  weak  current  in  the  wire 
of  the  armature ;  but  as  a  portion  of  this  current  is  carried  by  means 
of  a  shunt  wire  I  through  the  coil  of  the  field  magnet,  and  magnetizes 
the  core  more  strongly,  the  current  in  both  the  shunt  /  and  the  main 
wire  L  quickly  reaches  its  maximum. 

By  permission  of  the  United  States  Electric  Lighting  Company  we  in- 
troduce a  cut  (Fig.  179,  Plate  III.),  of  the  American  dynamo  called  the 
Weston.  It  will  be  seen  that  in  this  machine  a  powerful  field  magnet 
is  placed  on  each  side  of  the  revolving  armature.  A  steam-engine  com- 
municates motion  to  the  dynamo  by  means  of  a  belt  passing  over  the 


208  ELECTRICITY  AND   MAGNETISM. 

circumference  of  the  wheel  W,  and  causes  the  armature,  which  is  on  the 
axle  of  this  wheel,  to  revolve. 

183.  The  Dynamo  as  an  Electric-motor.  —  If,  instead  of 

expending  mechanical  energy,  such  as  that  of  a  steam-engine,  etc.,  in 
rotating  the  armature  of  a  dynamo,  a  current  from  another  dynamo  (or 
other  source)  is  sent  through  the  coil  of  its  armature,  the  armature  will 
rotate  under  the  action  of  the  electric  energy,  and  the  dynamo  thus 
becomes  an  electric-motor.  In  the  generating  dynamo  mechanical  energy 
is  transformed  into  electric  energy ;  in  the  receiving  dynamo  (used  as 
a  motor)  the  electric  energy  is  transformed  again  into  mechanical  energy. 
A  series  of  dynamos  (only  limited  in  number  by  the  loss  of  energy  by 
waste)  might  be  so  connected  that  transformation  in  each  is  the  reverse 
of  that  in  the  preceding. 

184.  Uses  of  Dynamos.  — We  live  at  the  interesting  epoch 
when  dynamos  are  being  rapidly  introduced  for  purposes  of  electric  light- 
ing, electroplating,  motive  power,  telegraphy,  charging  storage  batteries, 
etc.,  supplanting  to  a  large  extent  other  instrumentalities  and  branches  of 
industry,  much  as  sixty  years   ago  the   locomotive   commenced  its   dis- 
placement of  the  stage  coach. 

185.  Transmission  of  Electric  Energy. — One  of  the  most 
important  projects  which  is  enlisting  the  attention  of  electricians  at  the 
present  time  is  to  devise  some  efficient  means  of  economically  transform- 
ing, by  means  of  dynamos,  some  of  the  wasting  energies  of  nature,  such, 
for  example,  as  that  of  waterfalls,  into  electric  energy,  and  in  this  con- 
venient form  transferring  the  energy  through  wires  to  distant  and  availa- 
ble places,  such  as  large  cities,  where  it  may  be  transformed  by  lamps  into 
heat  and  light,  or  by  electric-motors  into  mechanical  energy  for  doing 
almost  any  kind  of  work.     The  project  is  theoretically  possible.     One  of 
the  principal  practical  difficulties  is  that  of  safely,  and  without  great  waste, 
transmitting  currents  of  great  magnitude  long  distances  through  conduc- 
tors such  as  are  now  in  use.     In  many  ways  electric  energy  is  one  of  the 
most  convenient  forms  of  energy;    hence   its  desirability  for  propelling 
street  cars,  for  operating  light  machinery,  etc.     It  is  apparent  that  if  this 
form  of  energy  could  somehow  be,  as  it  were,  bottled  up  or  stored  in  large 
quantities  in  a  small  space,  so  that  it  could  be  transported  easily  to  places 
where  it  is  needed,  it  would  be  a  valuable  achievement.     This  is  in  a 
measure  practicable  through  the  agency  of  the  so-called  "  storage  bat- 
teries." 


ELECTRIC   LIGHT.  209 

186.  Storage  Batteries.  —  The  storage  battery  is  virtually  an 
electrolysis  apparatus,  having  instead  of  two  platinum  electrodes  two 
lead  plates  coated  with  red  lead  (Pb304)  with  a  layer  of  paper  or  cloth 
between,  the  whole  suspended  in  dilute  sulphuric  acid.  (See  directions 
for  making  storage  batteries  in  the  author's  Physical  Technics,  page 
122.)  When  these  electrodes  are  connected  with  a  powerful  voltaic  bat- 
tery, or,  better,  with  a  dynamo,  the  +  electrode  becomes  peroxydized 
( PbO2)  by  the  oxygen  liberated  by  electrolysis,  while  the  —  electrode  is 
deoxydized  by  the  hydrogen  liberated.  In  other  words,  the  energy  of 
the  current  is  transformed  into  the  potential  energy  of  chemical  affinity. 
Note  that  it  is  an  electrical  storage  of  energy,  not  a  storage  of  electricity,  — 
two  very  different  things.  When  these  chemical  changes  have  progressed 
as  far  as  possible  the  battery  is  said  to  be  charged.  These  plates  may 
remain  for  many  days  in  this  condition,  if  the  circuit  is  left  open,  and 
may  be  transported  long  distances  and  used  in  the  same  way  and  for  the 
same  purposes  that  any  powerful  voltaic  battery  can  be  used.  Storage 
cells  may  be  combined  the  same  as  voltaic  cells  (which  in  fact  they  are 
after  charging),  and  with  similar  results.  Some  idea  of  the  capacity  of 
these  cells  may  be  formed  from  the  following  estimate.  In  a  cell  whose 
interior  dimensions  are  eight  inches  square  and  four  inches  deep,  there 
can  be  stored  up  energy  sufficient  to  furnish  one-half  of  a  horse-power 
working  for  an  hour. 


Section  XV. 

* 

USEFUL  APPLICATIONS  OF   ELECTRIC   ENERGY.  —  ELECTRIC 

LIGHT. 

The  applications  of  electric  energy  to  industrial  uses  are  so  numerous 
and  varied  that  the  limits  of  an  ordinary  text-book  on  general  Physics 
can  do  little  justice  to  the  subject,  and,  indeed,  a  description  of  the 
various  appliances  in  use  is  of  a  too  technical  character  to  come  properly 
within  the  scope  of  a  general  high-school  course.  Public  libraries  are 
now  well  provided  with  popular  works  relating  to  every  industrial  appli- 
cation. Students  may  consult  with  profit  such  books  as  Prescott's  The 


210  ELECTRICITY  AND  MAGNETISM. 

Telegraph  and  Telephone,  Dolbear's  The  Telephone,  Urquhart's  Electro- 
plating, S.  P.  Thompson's  Dynamo-Electric  Machinery,  and  Sawyer's 
Electric  Lighting. 

187.  Electric  Light:  Voltaic  Arc.  —  If  the  terminals 
of  wires  from  a  powerful  dynamo  or  galvanic  battery  are 
brought  together,  and  then  separated  1  or  2mm,  the  cur- 
rent does  not  cease  to  flow,  but  volatilizes  a  portion  of 
the  terminals.  The  vapor  formed  becomes  a  conductor 
of  high  resistance,  and  remaining  at  a  very  high  temper- 
ature produces  intense  light.  The  light  rivals  that  of  the 
sun  both  in  intensity  and  whiteness.  The  heat  is  so  great 
that  it  fuses  the  most  refractory  substances,  including  even 
the  diamond.  Metal  terminals  quickly  melt  and  drop  off 
like  tallow,  and  thereby  become  so  far  separated  that  the 
electro-motive  force  is  no  longer  sufficient  for  the  increased 
resistance,  and  the  light  is  extinguished.  Hence,  pencils 

of  carbon  (prepared 
from  the  coke  de- 
posited in  the  dis- 
tillation of  coal  in- 
side of  gas  retorts), 
rig.  iso.  being  less  fusible, 

are  used  for  terminals.  For  simple  experiments,  these 
pencils  may  be  held  in  forceps  (Fig.  180)  at  the  ends  of 
two  brass  rods,  to  which  the  battery  wires  are  attached. 
These  rods  slide  in  brass  heads,  A  and  B,  supported  by  in- 
sulating pillars,  so  that  the  distance  between  the  carbon 
points  may  be  regulated. 

The  light  is  too  intense  to  admit  of  examination  with 
the  naked  eye  ;  but  if  an  image  of  the  terminals  is  thrown 
on  a  screen  by  means  of  a  lens,  or  a  pin-hole  in  a  card,  an 
arch-shaped  light  is  seen  extending  from  pole  to  pole,  as 
shown  in  Figure  181.  This  light  has  received  the  name 


ELECTRIC   LIGHT. 


211 


Fig.  181, 


of  the  voltaic  arc.  The  larger  portion  of  the  light,  how- 
ever, emanates  from  the  tips  of  the  two  car- 
bon terminals,  which  are  heated  to  an  intense 
whiteness,  but  some  emanates  from  the  arc.  The 
+  pole  is  hotter  than  the  — pole,  as  is  shown  by 
its  glowing  longer  after  the  current  is  stopped. 
The  carbon  of  the  +  pole  becomes  volatilized, 
and  the  light-giving  particles  are  transported 
from  the  +pole  to  the  —pole,  forming  a  bridge 
of  luminous  vapor  between  the  poles.  What  we  see  is 
not  electricity,  but  luminous  matter. 

The  light  of  the  ordinary 
street  arc-lamp  has  an  inten- 
sity varying  from  one  to 
two  thousand  candle-power, 
or  the  combined  intensity  of 
from  fifty  to  a  hundred  ordi- 
nary gas-lights.  To  sustain 
such  a  light,  about  one  horse- 
power per  lamp  must  be  ap- 
plied at  the  dynamo. 

188.   Electric  Lamp.  —  It 

is  apparent  that  the  +  pole  is 
subject  to  a  wasting  away ; 
so  also  the  —  pole  wastes 
away,  but  not  so  fast.  At  the 
point  of  the  former  a  coni- 
cal-shaped cavity  is  formed, 
while  around  the  point  of 
the  latter  warty  protuber- 
ances appear.  When,  in  con-  Fls* 182' 
sequence  of  the  wearing  away  of  the  +  pole,  the  distance 


212 


ELECTRICITY   AND   MAGNETISM. 


between  the  two  pencils  becomes  too  great  for  the  elec- 
tric current  to  span,  the  light  goes  out.  Numerous  self- 
acting  regulators  for  maintaining  a  uniform  distance 
between  the  poles  have  been  devised.  Such  an  arrange- 
ment (Fig.  182)  is  called  an  electric  lamp.  The  move- 
ments of  the  carbons  arc  accomplished  automatically  by 
the  action  of  the  current  itself. 

The  difference  between  the  arc-lamps  of  the  various  in- 
ventors is  a  difference  in  the  mode  of  adjusting  or  "  feed- 
ing" the  carbons.  We  give  below  the  plan  of  the 


Fig.   183. 


Fig.  184. 


Fig.  185. 


189.  Brush  Lamp.  — The  current,  entering  at  A  (Fig.  183),  divides 
at  B  into  two  branches  which  pass  around  the  bobbin  C  in  opposite  direc- 
tions, one  branch  being  a  coarse  wire  of  low  resistance  and  in  the  same 
circuit  as  the  carbons,  and  the  other  branch  SS  being  a  shunt  of  high 
resistance,  connecting  the  terminals  B  and  G.  Inside  the  bobbin  is  a  soft 
iron  core,  F,  which  is  attached  to  the  upper  carbon.  When  a  current 
passes  through  the  two  branch  circuits  on  the  bobbin  C,  they  tend  to  mag- 
netize the  core  in  opposite  directions,  but  the  resistances  and  number  of 
turns  in  the  two  circuits  are  so  proportioned  that  the  magnetic  field  due  to 
the  low  resistance  branch  is  the  stronger,  and  the  core  F  is  therefore 


ELECTRIC    LIGHT. 


213 


drawn  up  into  the  bobbin,  lifting  the  upper  carbon  and  establishing  the 
arc.  Should  the  carbons  become  too  widely  separated  the  resistance  of 
the  arc,  and  consequently  of  the  coarse  wire  circuit  on  C,  increases,  dimin- 
ishing the  current  in  C  and  increasing  that  in  the  shunt  S.  The  field  due 
to  the  shunt  is  therefore  strengthened,  and  that  due  to  the  coarse  wire 
diminished,  allowing  the  core  F  to  fall  slightly,  bringing  the  carbons 
nearer  together.  By  the  device  of  the  two  opposing  fields,  due  to  the 
coils  on  C  being  wound  in  opposite  directions,  the  feeding  of  the  lamp  is 
done  automatically,  and  the  actual  distance  of  the  two  carbons  varies  but 
little. 

19O.  Incandescent  Electric  Lamps.  —  The  incandes- 
cent (or  "  glow ")  light  is  produced  by  the  heating  of 
some  refractory  body  to  a  state  of  incandescence  by  the 
passage  of  an  electric  current,  as,  for  example,  the  light 
given  off  by  heated  platinum  in  Experiment  120.  Plati- 
num is  little  used  for  this  purpose  on  account  of  its  lia- 
bility to  melt.  Carbon  filaments  are  now  exclusively 
used  in  incandescent  lamps.  In  the  Swan  lamp  (Fig.  184) 
a  filament  of  carbonized  cotton,  twisted  into  a  sort  of 
curl,  is  attached  at  its  ends  to  two  little  platinum  wires, 
a  and  5,  \vhich  have  previously  been  sealed  into  the  neck 
of  the  glass  bulb.  The  filament  of  the  Edison  lamp 
(Fig.  185)  is  carbonized  bamboo.  It  is  essential  that  the 
oxygen  of  the 
air  be  removed 
from  these  bulbs, 
otherwise  the  car- 
bons would  be 
quickly  burned 
out;  hence  very 
high  vacua  are 
produced  in  the 
bulbs  with  a  mercury  pump. 

An   Edison    16    candle-power   lamp    has    a   resistance    (when   hot)    of 
about  140  ohms,  the  difference  of  potential  at  its  terminals  is  about  100 


^Negative 


Fig.  186. 


214  ELECTRICITY    AND   MAGNETISM. 

volts,  and  it  requires  a  current   of  0.75  ampere.     Each  lamp  consumes 
about  one-tenth  of  a  horse-power. 

Incandescent  lamps  are  usually  introduced  into  the  circuit  in  multiple 
arc  (Fig.  186),  the  current  being  equally  divided  by  properly  regulating 
the  resistance  between  all  the  lamps  in  the  circuit. 


Section  XVI. 

USEFUL  APPLICATIONS   OF   ELECTRICITY  CONTINUED.  — 
ELECTROTYPING   AND    ELECTROPLATING. 

191.  Electrotyping.  —  This  book  is  printed  from  electrotype 
plates.  A  molding-case  of  brass,  in  the  shape  of  a  shallow  pan,  is  filled  to 
the  depth  of  about  one-quarter  of  an  inch  with  melted  wax.  A  few  pages 
are  set  up  in  common  type,  and  an  impression  or  mold'  is  made  by  press- 
ing these  into  the  wax.  The  type  is  then  distributed,  and  again  used  to 
set  up  other  pages.  Powdered  plumbago  is  applied  by  brushes  to  the  sur- 
face of  the  wax  mold  to  render  it  a  conductor.  The  case  is  then  sus- 
pended in  a  bath  of  copper  sulphate  dissolved  in  dilute  sulphuric  acid. 
The  —  pole  of  a  galvanic  battery  or  dynamo  machine  is  applied  to  it ;  and 
from  the  +  pole  is  suspended  in  the  bath  a  copper  plate  opposite  and  near 
to  the  wax  face.  The  salt  of  copper  is  decomposed  by  the  electric  cur- 
rent, and  the  copper  is  deposited  on  the  surface  of  the  mold.  The  sul- 
phuric acid  appears  at  the  +  pole,  and,  combining  with  the  copper  of  this 


ELECTROTYPING  AND  ELECTROPLATING. 


215 


pole,  forms  new  molecules  of  copper  sulphate.  When  the  copper  film 
has  acquired  about  the  thickness  of  an  ordinary  visiting  card,  it  is  removed 
from  the  mold.  This  shell  shows  distinctly  every  line  of  the  types  or 
engraving.  It  is  then  backed,  or  filled  in,  with  melted  type-metal,  to  give 
firmness  to  the  plate.  The  plate  is  next  fastened  on  a  block  of  wood, 
and  thus  built  up  type-high,  and  is  now  ready  for  the  printer.  (For  full 
directions  which  will  enable  a  pupil  to  electrotype  in  a  small  way,  see  the 
author's  Physical  Technics.) 

192.  Electroplating1. — The  distinction  between  electroplating 
and  electrotyping  is,  that  with  the  former  the  metallic  coat  remains  per- 
manently on  the  object  on  which  it  is  deposited,  while  with  the  latter  it  is 
intended  to  be  removed.  The  processes  are,  in  the  main,  the  same.  The 
articles  to  be  plated  are  first  thoroughly  cleaned  and  suspended  on  the 


Fig.  187. 

—  pole  of  a  battery,  and  then  a  plate  of  the  same  kind  of  metal  that  is  to 
be  deposited  on  the  given  articles  is  suspended  from  the  -f  pole  (Fig.  187). 
The  bath  used  is  a  solution  of  a  salt  of  the  metal  to  be  deposited.  The 
cyanides  of  gold  and  silver  are  generally  used  for  gilding  and  silvering. 
Many  of  the  base  metals  require  to  be  electro-coppered  first,  in  order  to 
secure  the  adhesion  of  the  gold  or  silver.  The  magneto-electric  machine 
has  almost  completely  replaced  the  voltaic  battery  for  electrotyping  and 
electroplating  purposes. 


216  ELECTRICITY   AND   MAGNETISM. 


Section  XVII. 

USEFUL   APPLICATIONS    OF   ELECTRIC    ENERGY   CON- 
TINUED. —  TELEGRAPHY. 

193.  The  Telegraph.  —  The  word  telegraph,  literally,  signifies  to 
write  far  away.  In  its  broadest  sense  it  embraces  all  methods  of  commu- 
nicating thought  with  great  speed  to  a  distance,  by  means  of  intelligible 
characters,  sounds,  or  signs ;  but  usually  it  is  applied  only  to  electrical 
methods. 

First,  it  should  be  understood  that,  instead  of  two  lines  of  wire,  one 
to  convey  the  electric  current  far  away  from  the  battery,  and  another 
to  return  it  to  the  battery,  if  the  distant  pole  is  connected  with 
a  large  metallic  plate  buried  in  moist  earth,  or,  still  better,  with  a 
gas  or  water  pipe  that  leads  to  the  earth,  and  the  other  pole  near 
the  battery  is  connected  in  like  manner  with  the  earth,  so  that  the  earth 
forms  about  one-half  of  the  circuit,  there  will  be  needed  only  one  wire 
to  connect  telegraphically  two  places  that  are  distant  from  each  other. 
Furthermore,  the  resistance  offered  by  the  earth  to  the  electric  current  is  prac- 
tically nothing ;  so  that,  disregarding  the  resistance  of  the  ground  connec- 
tions, there  is  a  saving  of  one-half  the  wire  and  one-half  the  resistance, 
and  consequently  of  one-half  the  battery  power. 

Let  B,  Figure  188,  Plate  IV.,  represent  the  message  sender,  or  operator's 
key;  Y,  the  message  receiver.  It  may  be  seen  that  the  circuit  is  broken 
at  B.  Let  the  operator  press  his  finger  on  the  knob  of  the  key.  He  closes 
the  circuit,  and  the  electric  current  instantly  fills  the  wire  from  Boston  to 
New  York.  It  magnetizes  a ;  a  draws  down  the  lever  b,  and  presses  the 
point  of  a  style  on  a  strip  of  paper,  c,  that  is  drawn  over  a  roller.  The 
operator  ceases  to  press  upon  the  key,  the  circuit  is  broken,  and  instantly 
b  is  raised  from  the  paper  by  a  spiral  spring,  d.  Let  the  operator  press 
upon  the  key  only  for  an  instant,  or  long  enough  to  count  one :  a  simple 
dot  or  indentation  will  be  made  in  the  paper.  But  if  he  presses  upon  the 
key  long  enough  to  count  three,  ^he  point  of  the  style  will  remain  in  contact 
with  the  paper  the  same  length  of  time ;  and,  as  the  paper  is  drawn  along 
beneath  the  point,  a  short  straight  line  is  produced.  This  short  line  is 
called  a  dash.  These  dots  and  dashes  constitute  the  alphabet  of  telegraphy. 
For  instance,  a  part  of  a  message,  "man  is  in,"  is  represented  as  printed 
in  telegraphic  characters  on  the  strip  of  paper.  The  Roman  letters  above 
interpret  their  meaning. 


Plate  IV. 


TELEGRAPHY.  217 

194.  The  Sounder.  —  If  the  strip  of  paper  is  removed,  and  the  style 
is  allowed  to  strike  the  metallic  roller,  a  sharp  click  is  heard.    Again,  when 
the  lever  is  drawn  up  by  the  spiral  spring,  it  strikes  a  screw  point  above 
(not  represented  in  the  figure),  and  another  click,  differing  slightly  in 
sound  from  the  first,  is  heard.     A  listener  is  able  to  distinguish  dots  from 
dashes  by  the  length  of  the  intervals  of  time  that  elapse  between  these  two 
sounds.     Operators  generally  read  by  ear,  giving  heed  to  the  clicking 
sounds  produced  by  the  strokes  of  a  little  hammer.     A  receiver  so  used  is 
called  a  sounder,  a  common  form  of  which  is  represented  in  the  lower  cen- 
tral part  of  Plate  IV. 

195.  The  Relay  and  the  Repeater.  —  The  strength  of  the  cur- 
rent is  diminished,  of  course,  as  the  line  is  extended  and  the  number  of  in- 
struments in  the  circuit  is  increased.     Hence,  a  current  that  would  move 
the  parts  of  a  single  sounder  audibly,  on  a  short  line,  would  not  move  the 
same  parts  of  many  sounders  on  a  long  line  with  sufficient  force  to  render 
the  message  audible.     Resort  is  had  to  re/ays  and  repeaters. 

In  Figure  189,  Plate  IV.,  the  letter  R  represents  a  relay  and  S  a  sounder. 
Suppose  a  weak  current  arrives  at  New  York  from  Boston,  and  has  suffici- 
ent strength  to  attract  the  armature  of  the  relay  at  that  station.  This,  as 
may  be  seen  by  examination  of  the  diagram,  will  close  another  short  circuit, 
called  the  local  circuit,  and  send  a  current  from  a  local  battery  located  in  the 
same  office  through  the  sounder  at  that  station.  The  sounder,  being  op- 
erated by  a  battery  in  a  circuit  of  only  a  few  feet  in  length,  delivers  the 
message  audibly.  If  it  is  desired  that  the  message  should  go  beyond  New 
York,  —  for  instance,  to  Philadelphia,  —  then  we  have  only  to  suppose  the 
lo'-al  line  at  New  York  to  be  lengthened  so  as  to  extend  to  Philadelphia, 
and  a  powerful  line  battery  to  be  substituted  for  the  small  local ;  then  the 
message  that  leaves  Boston  will  be  shifted  from  one  circuit  to  the  other  at 
New  York,  and  be  delivered  in  Philadelphia  without  the  intervention  of 
any  operator  on  the  route.  In  this  case  a  relay  is  called  a  repeater.  The 
electro-magnets  in  relays  are  wound  with  long,  thin  wire,  while  those 
of  sounders  are  wound  with  short,  large  wire.  The  main  battery  consists 
of  many  cells  in  series.  It  may  be  located  at  either  terminus,  but  it  is 
generally  split  in  halves,  and  one  half  placed  at  each  terminus. 

In  the  diagram,  the  circuit  is  represented  as  open  at  both  keys.  When 
the  line  is  not  in  use,  the  circuit  ought  always  to  be  left  closed,  by  means 
of  switches  connected  with  the  keys  (not  represented  in  the  diagram),  so 
that  when  the  line  is  not  "  at  work  "  an  electric  current  is  constantly  trav- 
ersing the  wire.  Sending  a  message,  consequently,  consists  in  interrupting 
this  current  by  means  of  a  key.  Suppose  that  Boston  wishes  to  communi- 


218  ELECTRICITY   AND   MAGNETISM. 

cate  with  New  York.  He  first  removes  the  switch  on  his  key,  which  breaks 
the  circuit  and  enables  him  to  control  the  circuit  with  his  key.  He  then 
manipulates  his  key  so  as  to  produce  an  understood  signal,  which  will  at- 
tract New  York's  attention.  Every  time  that  Boston  presses  on  his  key, 
every  armature  in  his  own  office,  and  in  the  New  York  office,  and  at  way 
stations,  falls.  Of  course  the  message  may  be  read  at  every  station  on  the 
route. 

TELEGRAPHIC  ALPHABET. 
A  B  C  D  E  F 

G  H  I  J  K  L 

M  N  O  P  Q  R 

8  T  U  V  W  X 

T  Z  &  ,  ? 


TELEGRAPHIC  FIGURES. 
234 


7 


Section  XVIII. 

USEFUL    APPLICATIONS    OF    ELECTRIC    ENERGY    CON- 
TINUED. —  TELEPHONY. 

196.  Bell  Telephone.— Figure  190  represents  a  sectional  and  a 
perspective  view  of  this  instrument.  It  consists  of  a  steel  magnet  A, 
encircled  at  one  extremity  by  a  spool  B  of  very  fine  insulated  wire,  the 
ends  of  which  are  connected  with  the  binding-screws  DD.  Immediately 
in  front  of  the  magnet  is  a  thin  circular  iron  disk  EE.  The  whole  is  en- 
closed in  a  wooden  or  rubber  case  F.  The  conical-shaped  cavity  G  serves 
the  purpose  of  either  a  mouth-piece  or  an  ear-trumpet.  There  is  no  dif- 
ference between  the  transmitting  and  receiving  telephone;  consequently 


TELEPHONY.  219 

either  instrument  may  be  employed  as  a  transmitter,  while  the  other  serves 
as  a  receiver.  Two  magneto  telephones  in  a  circuit  are  virtually  in  the 
relation  of  a  dynamo  and  a  motor.  The  transmitter  being  in  itself  a 
diminutive  dynamo,  of  course  no  battery  is  required  in  the  circuit.  Con- 
nect in  circuit  two  such  telephones,  and  the  apparatus  is  ready  for  use. 

When  a  person  talks  near  the  disk  of  the  transmitter,  he  throws  it  into 
rapid  vibration.  The  disk,  being  quite  close  to  the  magnet,  is  magnetized 
by  induction ;  and  as  it  vibrates,  its  magnetic  power  is  constantly  chang- 


Fig.  190. 

ing,  being  strengthened  as  it  approaches  the  magnet,  and  enfeebled  as  it 
recedes.  This  fluctuating  magnetic  force  will  of  course  induce  currents 
in  alternate  directions  in  the  neighboring  coil  of  wire.  These  currents 
traverse  the  whole  length  of  the  wire,  and  so  pass  through  the  coil  of  the 
distant  instrument.  When  the  direction  of  the  arriving  current  is  such  as 
to  re-enforce  the  power  of  the  magnet  of  the  receiver,  the  magnet  attracts 
the  iron  disk  in  front  of  it  more  strongly  than  before.  If  the  current  is  in 
the  opposite  direction,  the  disk  is  less  attracted,  and  flies  back.  Hence, 
whatever  movement  is  imparted  to  the  disk  of  the  transmitting  telephone, 
the  disk  of  the  receiving  telephone  is  forced  to  repeat.  The  vibrations  of 
the  latter  disk  become  sound  in  the  same  manner  as  the  vibrations  of  a 
tuning-fork  or  the  head  of  a  drum. 

The  above  is  a  description  of  the  original  and  simplest  form  of  the 
Bell  telephone.  It  is  apparent  that  the  original  energy,  i.e.  that  of  the 
voice,  applied  at  the  transmitter  must,  during  its  successive  transforma- 


220 


ELECTRICITY    AND   MAGNETISM. 


tions  and  especially  during  its  transmission  in  the  form  of  electric  energy 
through  large  resistances,  become  very  much  enfeebled,  so  that  when  it 
reappears  as  sound,  the  sound  is  quite  feeble  and  frequently  inaudible. 
The  first  grand  improvement  on  the  original  consists  in  introducing  a  bat- 
tery into  the  circuit,  and  so  arranging  that  the  voice,  instead  of  being 
obliged  to  generate  currents,  should  be  required  to  act  only  as  a  controlling 
force  of  a  current  already  generated  by  the  battery.  It  is  evident  that 
only  a  fluctuating  or  undulating  current  can  produce  the  necessary  vibra- 
tions in  the  disk  of  the  receiver.  The  fluctuations  are  caused  by  a  varv- 


Fijr.  191. 


Fig.  193. 

ing  resistance  in  the  circuit.  The  pupil  must  have  learned  by  experience 
ere  this  that  the  effect  of  a  loose  contact  between  any  two  parts  of  a  cir- 
cuit is  to  increase  the  resistance  and  thereby  weaken  the  current ;  but  the 
effect  of  a  slight  variation  in  pressure  is  especially  noticeable  when  either 
or  both  of  the  parts  are  carbon.  Figure  101  illustrates  a  simple  telephonic- 
circuit  in  which  are  included  a  variable  resistance  transmitter  T,  a  mag- 
neto receiver  R,  and  a  battery  B.  '  One  of  the  electrodes,  a  platinum 
point,  touches  the  center  of  the  transmitter  disk ;  the  other  electrode,  a 
carbon  button  a,  is  pressed  by  a  spring  gently  against  the  platinum  point. 
Every  vibration  of  the  disk,  however  minute,  causes  a  variation  in  the 
pressure  between  the  two  electrodes  and  a  corresponding  variation  in  the 
circuit  resistance.  As  changes  the  resistance,  so  changes  the  current 


TELEPHONY. 


221 


strength,  and  so  consequently  changes  the  force  with  which  the  magnet 
in  the  receiver  R  pulls  its  disk.     The  vary- 
ing tension  between  magnet  and  disk  causes 
the  latter  to  vibrate  and  reproduce  sounds. 

The  next  improvement  of  considerable 
importance  consists  in  the  adoption  of  an 
induction  coil,  which,  we  have  learned,  pro- 
duces a  current  of  much  greater  electro- 
motive force  than  is  possessed  by  the  original 
battery  current.  By  its  adoption  we  are  able 
to  converse  over  much  longer  distances,  and 
since  the  battery  current  traverses  only  a 
local  circuit,  as  may  be  seen  by  reference  to 
Figure  192,  a  single  Leclanche  cell  is  gener- 
ally sufficient  to  operate  it.  The  currents 
induced  by  the  fluctuating  primary  current 
traverse  the  line  wire  and  generate  sonorous 
vibrations  in  the  disk  of  the  receiver  in  the 
same  manner  as  in  the  original  telephone. 

Figure  193  represents  the  entire  tele- 
phonic apparatus  required  at  any  single 
station.  The  box  A  contains  a  small  hand- 
dynamo,  such  as  is  represented  in  Figure 
194.  A  person  turning  the  crank  F  gener- 
ates a  current  which  rings  a  pair  of  elec- 
tric bells  G,  both  at  his  own  and  at  a  dis- 
tant station,  and  thus  attracts  attention.  He 
next  takes  the  receiver  B  off  the  supporting 
hook  and  places  it  to  his  ear.  When  the 
weight  is  removed  from  the  hook,  the 
hook  rises  a  little  and  throws  the  dynamo 
and  bells  out  of  the  circuit,  and  at  the 
same  time  introduces  the  receiver  B,  the 
transmitter  C,  and  the  battery  D,  so  that  the 
circuit  stands  as  represented  in  Figure  192. 
The  box  C  contains  the  induction  coil.  E 
is  a  "lightning  arrester." 


Fig.  193. 


197.  Microphone.  —  In  Figure  195, 
A  and  B  are  buttons  of  carbon  ;  the  former 
is  attached  to  a  sounding-board  of  thin 


Fig.  194. 


222 


ELECTRICITY   AND    MAGNETISM. 


pine  wood,  the  latter  to  a  steel  spring  C,  and  both  are  connected  in 
circuit  with  a  battery  and  a  telephone  used  as  a  receiver.  The  spring 
presses  B  against  A,  and  any  slight  jar  will  cause  a  variation  in  the 
pressure  and  corresponding  variations  in  the  current  strength. 


By  means  of  this  instrument,  called  the  microphone,  any  little  sounds,  as 
its  name  indicates,  such  as  the  ticking  of  a  watch  or  the  footfall  of  an 
insect,  may  be  reproduced  at  a  considerable  distance,  and  be  as  audible  as 
though  the  original  sounds  were  made  close  to  the  ear. 


Section  XIX. 

THERMO-ELECTRIC    CURRENTS. 

198.    Heat  Energy  transformed  directly  into  Electric 
Energy. 

Experiment  170.  —  Insert  in  one  screw-cup  of  an  astatic  galvan- 
ometer an  iron  wire,  and  in  the  other  cup  a  copper,  or  better,  a  Ger- 


THERMO-ELECTRIC   CURRENTS.  228 

man  silver  wire.  Twist  the  other  ends  of  the  wire  together,  and  heat 
them  at  their  junction  in  a  flame;  a  deflection  of  the  needle  shows 
that  a  current  of  electricity  is  traversing  the  wire.  Place  a  piece  of 
ice  at  their  junction;  a  deflection  in  the  opposite  direction  shows 
that  a  current  now  traverses  the  wire  in  the  opposite  direction. 

Experiment  171.  —  Take  a  strip  of  sheet  copper  about  15  inches 
long  and  three-fourths  of  an  inch  wide,  and  a  strip  of  zinc  of  the  same 
dimensions.  Lay  them  one  upon  the  other,  and  fold  over  each  end 
upon  itself  for  about  half  an  inch,  and  hammer  the  joints  flat,  so  that 
they  shall  hold  together  quite 
firmly.  Then  separate  the  two 
strips  into  a  somewhat  elliptical 
or  rectangular  shape,  as  shown  in 
Figure  196.  Cut  a  hole  through 
the  center  of  one  of  the  strips, 
and  pass  the  wire  support  of 
a  magnetic  needle  through  it.  Fis-  196. 

Place  the  band  in  the  magnetic  meridian  parallel  with  the  needle. 
Direct  a  flame  against  one  of  the  junctions,  and  note  the  deflection, 
and  determine  the  direction  in  which  the  current  traverses  the  band, 
i.e.  whether  the  current  passes  from  the  heated  junction  through  the 
copper  or  the  zinc  strip. 

These  currents  are  named,  from  their  origin,  thermo- 
electric. The  apparatus  required  for  the  generation  of 
these  currents  is  very  simple,  consisting  merely  of  bars  of 
two  different  metals  joined  at  one  extremity,  and  some 
means  of  raising  or  lowering  their  temperature  at  their 
junction,  or  of  raising  the  temperature  at  one  extremity 
of  the  pair  and  lowering  it  at  the  other ;  for  the  electro- 
motive force,  and  consequently  the  strength  of  the  cur- 
rent, is  nearly  proportional  to  the  difference  in  tempera- 
ture of  the  two  extremities  of  the  pair.  The  strength  of 
the  current  is  also  dependent,  as  in  the  voltaic  pair,  on 
the  thermo-electromotive  force  of  the  metals  employed. 
The  following  thermo-electric  series  is  so  arranged  that  if 
the  temperatures  of  both  junctions  are  near  the  ordinary 


224 


ELECTRICITY   AND    MAGNETISM. 


temperatures  of  the  air,  those  metais  farthest  removed 
from  each  other  give  the  strongest  current  when  com- 
bined ;  and  the  current  passes,  when  heated  at  their  junc- 
tion, from  the  one  first  named  to  that  succeeding  it.  The 
arrows  indicate  the  direction  of  the  current  at  the  heated 
and  the  cold  ends  respectively.  At  high  temperatures  the 
current  may  be  reversed. 


Cold. 


I     1 
g      3 


a    -I 


&    J5     ~     .5 

O       AH       02 


N      I 


Heat. 
199.    Thermo-electric  Batteries  and  Thermo-pile. — 

The  electro-motive  force  of  the  thermo-electric  pair  is  very 
small  in  comparison  with  that  of  the  voltaic  pair ;  hence 
the  greater  necessity  of  combining  a  large  number  of  pairs 
with  one  another  in  series.  This  is  done  on  the  same 
principle,  and  in  the  same  manner,  that  voltaic  pairs  are 
united ;  viz.,  by  joining  the  +  metal  of  one  pair  to  the 
—  metal  of  another.  Figure  197  represents 
such  an  arrangement.  The  light  bars  are 
bismuth,  and  the  dark  ones  antimony.  If 
the  source  of  heat  is  strong  and  near,  one 
face  may  be  heated  much  hotter  than  the 
other,  and  a  current  equal  to  that  from  an 
ordinary  galvanic  cell  is  often  obtained. 
Fig.  197.  Such  contrivances  for  generating  electric 
currents  are  called  thermo-electric  batteries.  They  are 
seldom  used,  inasmuch  as  the  best  of  them  transform  less 
than  one  per  cent  of  the  heat  energy  given  out  by  the 
source  of  heat. 


STATIC   ELECTBICITY.  225 

If  the  source  of  heat  is  feeble  or  distant,  the  feeble  cur- 
rent may  serve  to  measure  the  difference  of  temperature 
between  the  ends  of  the  bars  turned  toward  the  heat  and  the 
other  ends,  which  are  at  the  temperature  of  the  air.  The 
apparatus,  when  used  for  this  purpose, 
is  called  a  thermo-pile,  or  a  thermo- 
multiplier.  A  combination  (Fig.  198) 
of  as  many  as  thirty-six  pairs  of  anti- 
mony and  bismuth  bars,  connected  with 
a  very  sensitive  galvanometer,  consti- 
tutes an  exceedingly  delicate  thermoscope 
and  thermometer.  Changes  of  tempera- 
ture that  would  not  produce  a  percep-  Fig.  198. 
tible  change  in  an  ordinary  thermometer,  can,  by  the 
use  of  a  thermo-electric  pile,  be  made  to  produce  large 
deflections  of  the  galvanometer  needle.  Heat  radiated 
from  the  body  of  an  insect  several  inches  from  the  pile 
may  cause  a  sensible  deflection. 


Section  XX. 

STATIC    ELECTRICITY. 

2OO.  Mechanical  Energy  transformed  into  Electric 
Potential  Energy  or  Electrification. 

Experiment  172.  —  Prepare  an  insulated  stool  (Fig.  199)  by  plac- 
ing a  square  board  on  four  dry  and  clean  glass  tumblers,  used  as  legs. 
Let  a  person,  whom  we  will  call  John,  stand  on  this  stool,  and  let  a 
second  person,  James,  strike  John  a  few  times  with  a  cat's  fur.  Then 
let  James  bring  the  knuckle  of  a  finger  near  to  some  part  of  John's 


226 


ELECTRICITY   AND   MAGNETISM. 


person,  for  instance  his  hand,  chin,  or  nose ;  an  electric  spark  will 
pass  between  the  two,  and  both  will  experience  a  slight  shock.  The 
length  of  the  spark  shows  that  the  electricity  is  urged  by  a  high 
E.M.F.,  like  the  induced  currents  of  the  magneto-machine  and  in- 
duction coil. 

As  mechanical  energy  is  transformed  into  potential 
energy  in  the  act  of  bending  a  bow  or  stretching  a  rub- 
ber band,  in  other 
words,  a  peculiar 
molecular  stress  is 
developed  thereby, 
so  by  the  expendi- 
ture of  mechanical 
energy  in  separating 
the  fur  from  the  boy 
at  the  end  of  each 
stroke  there  is  de- 
veloped a  phase  of 
potential  energy;  the 
Fig.  199.  bodies  in  which  it  is 

developed  are  said  to  be  in  a  state  of  electrification,  in 
other  words,  there  exists  between  them  a  form  of  electric 
stress.  The  electrified  bodies  are  sometimes  said  to  be 
"  charged  "  with  electricity. 


2O1.    Electroscope. 

Experiment  173.  —  Suspend  in  a  loop,  tied  in  a  white  silk  thread, 
a  strip  of  "  Dutch  metal,"  so  that  the  two  vertical  por- 
tions  may  be  near  each  other.  After  John  has  been 
struck  a  few  times  with  the  fur,  let  him  bring  a  finger 
gradually  near  the  upper  extremity  of  the  foil;  the  two 
//\  portions  of  the  foil  gradually  diverge,  as  in  Figure 

s/\^  200,  indicating  the  action  of  an  unusual  force  between 

Fie-*°°-     them. 


STATIC    ELECTRICITY. 


22T 


Any  arrangement,  like  that  of  the  foil  just  described, 
intended  to  detect  the  presence  of  electrification,  is  called 
an  electroscope.  One  of  the  most  common  and  useful 
electroscopes  consists  of  one  or  two  pith-balls,  made  from 
the  pith  of  elder  or  sunflower,  suspended  by  silk  thread. 
If  an  electroscope  is  brought  near  to  either  pole  of  a  sec- 
ondary wire  of  an  induction  coil,  a  similar  electrification 
is  manifested  by  the  poles.  Likewise,  by  means  of  very 
delicate  electroscopes,  the  poles  of  a  galvanic  battery,  or 
of  a  thermo-battery,  are  found  to  be  feebly  electrified. 

202.  Attractions  and  Repulsions. 

Experiment  174.  —  Poise  a  flat  wooden  ruler  on  an  inverted  bottle 
or  flask,  having  a  round  bottom,  as  in 
Figure  201.  Draw  a  rubber  comb  two 
or  three  times  through  your  hair,  or 
rub  it  with  a  woollen  cloth,  and  place 
it  near  one  end  of  the  ruler ;  instantly 
the  ruler  moves  toward  the  comb. 

Experiment  175.  —  Hold  the  comb 
over  a  handful  of  bits  of  tissue  paper; 
the  papers  quickly  jump  to- the  comb, 
stick  to  it  for  an  instant,  and  then  leap 
energetically  from  the  comb.  The 
papers  are  first  attracted  to  the  comb, 
but  in  a  short  time  acquire  some  of  its 
electrification,  and  then  are  repelled. 

Experiment  176.  —  Support  a  plate 
of  window  glass  (Fig.  202)  about  two 
inches  from  a  table.  Rub  its  upper 
surface  with  a  silk  handkerchief,  and 
place  pith-balls  or  bits  of  tissue  paper  on  the  table  beneath  the  glass. 
They  will  dance  up  and  down  between  the  plate  and  table  in  a  lively 
manner. 

203.  Two  States  of  Electricity.  —  It  is  quite  apparent 
that  we  are  now  dealing  with    a   very   different    class  of 


Fig.  201. 


Fig.  202. 


228  ELECTRICITY   AND    MAGNETISM. 

electrical  phenomena  from  any  that  we  have  previously 
observed.  It  is  also  quite  as  obvious  that  we  are  dealing 
with  electricity  in  a  very  different  state  or  condition  from 
that  in  which  we  have  before  studied  it.  Hitherto  we 
have  studied  only  those  phenomena  produced  by  electric- 
ity when  in  motion ;  and,  inasmuch  as  when  in  that  state 
its  energy  is  expended  in  work,  or  transformed  into  some 
other  form  of  energy  as  rapidly  as  it  is  generated,  there 
was  no  such  thing  as  an  accumulation  of  electricity.  In 
our  late  experiments  there  is  wanting  anything  like  a  cur- 
rent ;  but,  on  the  other  hand,  we  find  that  electricity  in 
this  new  state  may  accumulate,  be  stored  up,  and  remain 
in  a  quiescent  state  for  an  indefinite  time.  In  the  latter 
state  it  is  incapable  of  affecting  a  magnetic  needle,  mag- 
netizing, generating  heat,  illuminating,  producing  decom- 
position, or  giving  shocks.  But  in  this  state  of  apparent 
repose  it  may  attract  and  afterwards  repel  light  bodies  in 
the  vicinity  of  the  body  in  which  it  resides.  These  attrac- 
tions and  repulsions  are  quite  distinct  from  the  attractions 
and  repulsions  which  occur  between  parallel  currents. 

This  state  of  electricity  is  called  static,  in  distinction 
from  the  current  state,  which  Is  often  called  dynamic. 
We  have  seen  that,  under  certain  conditions,  electricity 
may  change  from  one  state  to  the  other,  as  when  the  elec- 
tricity which  had  accumulated  in  the  boy  on  the  insulated 
stool  passed  to  the  other  boy,  producing,  in  its  current 
state,  both  illuminating  and  physiological  effects ;  and 
again,  when  a  circuit  is  broken,  the  current  ceases,  but 
electricity  accumulates  in  the  wire.  We  have  also  learned 
that  electricity  of  high  E.M.F.,  such  as  is  most  readily 
developed  by  friction,  exhibits  the  static  phenomena,  i.e. 
attractions  and  repulsions,  most  strikingly. 


STATIC   ELECTRICITY. 


229 


2O4.    Two  Kinds  of  Electrification. 

Experiment  177.  —  Bend  a  small  glass  tube  into  the  form  repre- 
sented by  A  (Fig.  203),  insert  one  end  in  a  block  of  wood  B  for  a 
base ;  and  suspend  from  the  tube  a  pith-ball  C  by  a  silk  thread.  Rub 
a  glass  rod  D  with  a  silk  handkerchief,  and  present  it  to  the  ball ; 
attraction  at  first  occurs,  followed  by  repulsion  after  contact.  Now 
rub  a  stick  of  sealing-wax,  or  a  hard-rubber  ruler,  with  flannel,  and 
present  it  to  the  ball,  which  is  in  a  condition  such  that  it  is  repelled 
by  the  electrified  glass ;  it  is  attracted  by  the  electrified  sealing-wax. 
We  are  led  to  suspect  that  the  sealing-wax  possesses  a  different  kind 

of  electrification  from  that 
of  the  glass.  Let  us  fur- 
ther test  the  matter. 


Fig.  203. 


Fig.  204. 


Experiment  178.  —  Suspend  two  glass  rods  that  have  each  been 
rubbed  with  silk  in  two  wire  stirrups  (Fig.  204),  and  present  them  to 
each  other ;  they  repel  one  another.  Suspend  two  sticks  of  sealing- 
wax  that  have  been  rubbed  with  flannel  in  the  same  manner;  the 
same  result  follows.  Now,  in  a  like  manner,  present  one  of  the  glass 
rods  and  one  of  the  sticks  of  sealing-wax  to  each  other ;  they  attract 
one  another. 


It  is  evident  (1)  that  there  are  two  kinds  or  conditions  of 
electrification,  or,  for  convenience,  we  sometimes  say  two 
kinds  of  electricity ;  (2)  that  they  are  so  related  to  each 
other  that  like  kinds  repel,  and  unlike  kinds  attract  each 
other.  The  two  kinds  are  usually  distinguished  from 
each  other  by  the  names  positive  and  negative,  or,  more 
briefly,  as  +E  and  —  E.  The  former  is,  by  definition, 


230 


ELECTRICITY   AND   MAGNETISM. 


such  as  is  developed  on  glass  when  rubbed  with  silk,  and 
the  latter  is  the  kind  developed  on  sealing-wax  when 
rubbed  with  flannel.  There  is  no  reason,  except  custom, 
for  calling  the  one  positive  rather  than  the  other. 

Experiment  179.  —  Once  more  electrify  a  stick  of  sealing-wax  with 
a  flannel,  and  present  it  to  a  pith-ball,  and  after  the  ball  is  repelled, 
bring  the  surface  of  the  flannel  which  had  electrified  the  rod  near 
the  ball ;  the  ball  is  attracted  by  it,  showing  that  the  rubber  is  also 
electrified  and  with  the  opposite  kind  to  that  which  the  sealing-wax 


One  kind  of  electrification  is  never  developed  alone; 
when  two  bodies  are  rubbed  together  they  become  equally  but 
oppositely  electrified. 


Fig.  205. 

2O5.    Induction. 

Experiment  180.  —  Suspend  by  silk  threads  from  a  glass  tube 
two  egg-shells  covered  with  tin  foil,  so  as  to  touch  each  other,  as  in 
Figure  205.  Bring  near  to  one  end  of  the  shells,  but  not  to  touch,  a 
sealing-wax  rod  excited  with  flannel,  and  therefore  having  —  E.  While 
the  rod  is  in  this  position,  carry  a  thin  strip  of  tissue  paper,  or  a  pith- 
ball  suspended  by  a  silk  thread,  along  the  eggs.  The  paper  is  attracted 
most  strongly  at  the  ends ;  but  in  the  middle,  where  the  shells  are  in 
contact,  there  is  very  little  electrification.  Separate  B  from  A  about 


STATIC   ELECTRICITY.  231 

}  while  the  rod  D  is  still  in  position.  Then  place  D  midway  be- 
tween A  and  B;  the  rod  repels  B  and  attracts  A.  It  appears  that 
when  the  two  shells  touched  each  other,  thereby  constituting  practi- 
cally one  body,  that  the  shells  were  oppositely  electrified,  as  repre- 
sented by  the  signs  +  and  —  in  the  diagram  ;  and  when  the  two  bodies 
were  separated,  they  retained  their  opposite  charges. 

We  learn  from  this  experiment  that  by  induction  we 
may  charge  at  the  same  time  two  bodies,  one  with  +  E 
and  the  other  with  —  E. 

2O6.    Discharge. 

Experiment  181.  —  Bring  the  two  shells  oppositely  charged  near 
each  other;  when  near  enough  they  exhibit  mutual  attraction  for 
each  other.  On  bringing  them  still  nearer,  a  spark  passes  between 
them,  their  mutual  attraction  suddenly  ceases,  and  on  testing  them 
with  an  electroscope,  it  is  found  that  both  have  lost  their  electrifica- 
tion, i.e.  both  have  become  discharged. 

When  two  bodies  equally  and  oppositely  electrified  are  brought  together,  both 
become  discharged.  During  the  process  of  discharge,  the  electricity  which 
was  previously  in  a  condition  of  rest,  or  a  static  state,  assumes  a  condition 
of  motion,  or  a  dynamic  state,  as  is  shown  by  a  spark  passing  between 
the  two  bodies  when  brought  near  each  other.  One  of  the  bodies  (that 
positively  charged)  is  at  a  potential  higher  than  that  of  the  earth,  the  other 
is  at  a  lower  potential.  When  they  are  brought  sufficiently  near,  the  ten- 
dency of  the  electricity  to  pass  from  the  region  of  higher  potential  becomes 
strong  enough  to  penetrate  the  insulating  air  and  establish  a  condition  of 
equilibrium.  In  this  particular  case  the  result  is  zero  potential  or  no  elec- 
trification; but  in  general  both  bodies  would  be  left  at  a  like  condition  of 
electrification,  its  sign  depending  upon  the  sign  of  that  electricity  which 
was  in  excess, 

We  may  now  understand  how  it  is  that  an  electrified  body  attracts  to 
itself  light  bodies  in  its  vicinity.  For  example,  a  stick  of  sealing-wax, 
excited  with  —  E,  brought  near  a  pith-ball,  induces  +  E  next  itself,  and 
repels  —  E  to  its  farthest  side  ;  then,  of  course,  attraction  follows.  There 
is  the  same  attraction  between  heavy  bodies,  but  usually  not  sufficient  to 
produce  motion. 


232  ELECTRICITY   AND   MAGNETISM. 

2O7.  Insulation.  —  A  body  that  is  to  receive  a  perma- 
nent charge  of  electricity  must  be  insulated,  i.e.  have  no 
connection  with  the  earth  through  a  conducting  sub- 
stance. Some  of  the  best  insulating  substances  are  dry 
air,  ebonite,  shellac,  resins,  glass,  silks,  mid  furs.  Moisture 
injures  the  insulation  of  bodies;  hence  experiments  suc- 
ceed best  on  dry,  cold  days  of  winter,  when  moisture  of 
the  air  is  least  liable  to  be  condensed  on  the  surfaces  of 
apparatus,  especially  if  they  are  kept  warm. 


Section  XXI. 

ELECTRICAL  MACHINES.  —  CONDENSERS,    ETC. 

2O8.  Plate  Machine.  —  An  electrical  machine  is  an 
instrument  intended  for  transforming  mechanical  energy 
into  the  energy  of  electrification.  The  plate  machine 
(Fig.  206)  consists  of  a  conductor  A,  a  glass  plate  B,  a 
rubber  C  made  of  two  cushions  covered  with  a  prepara- 
tion which  facilitates  the  excitation,  and  a  brass  chain 
E  used  to  connect  the  cushions  with  the  earth.  An 
extension  of  the  conductor  consists  of  a  comb  D  whose 
pointed  teeth  are  turned  towards  the  plate.  When  the 
plate  is  turned  in  the  direction  indicated  by  the  arrow, 
it  passes  between  the  rubbers,  and  the  friction  causes 
4-  E  to  collect  on  the  plate  and  -  E  on  the  rubber. 
The  electrified  portion  of  the  plate  then  comes  opposite 
the  comb,  when  it  polarizes  the  conductor,  attracting 
—  E  and  repelling  +  E.  But  the  —  E  escapes  from  the 


ELECTRICAL  MACHINES. 


233 


points  of  the  comb  to  the  plate,  neutralizes  the  +  E  of  the 
plate,  and  thereby  leaves  the  conductor  charged  with  -f-  E. 


Fig.  206. 

2O9.  Electrophorus.  —  This  apparatus  is 
used  to  incite  electrification  by  induction.  It  con- 
sists of  a  shallow  iron  dish  A  (Fig.  207)  filled 
with  sealing-wax.  At  the  center  of  the  dish  is 
a  protuberance  B  which  extends  just  through 
the  wax.  A  flat  brass  disk  C  has  a  glass  insu- 
lating handle. 

Experiment  182.  —  Strike  the  surface  of  the 
wax  a  few  times  with  a  cat's  fur,  or  rub  it  with 
a  dry  flannel.  The  wax  becomes  electrified  with 
-  E.  Place  the  disk  C  upon  it.  The  +  E  of  the 
disk  is  bound  (i.e.  held  by  the  attraction  of)  the 
—  E  of  the  wax,  but  the  —  E  of  the  disk  is  re- 
pelled by  the  —  E  of  the  wax  and  passes  through 
the  protuberance  B  to  the  dish  below,  and  m%' 

thence  to  the  earth.     Consequently  when  the  disk  C  is  raised  by 


234  ELECTRICITY  AND  MAGNETISM. 

the  insulating  handle  from  the  wax,  it  is  charged  with  +  E,  and  the 
charge  can  be  transferred  to  any  body  (e.g.  a  Leyden  jar),  and  then 
the  disk  can  be  recharged  by  replacing  it  on  the  wax.  This  may 
be  repeated  many  times  without  sensibly  reducing  the  inductive 
power  of  the  wax. 

The  Holtz  machine  (Fig.  139)  is  a  sort  of  a  continuous  electroph- 
orus  which  is  capable  of  developing  electrification  by  induction  so 
rapidly  and  continuously  as  to  give  an  almost  incessant  flow  of  sparks 
between  the  two  conductors. 

210.  Condenser.  —  A   very  important   adjunct  to  an 
electrical  machine  is  a  condenser  of  some  kind,  by  means 
of  which  a  large  quantity  of  electricity  can  be  collected 
on  a  small  surface. 

Experiment  183.  —  Let  a  person  stand  on  an  insulated  stool 
(page  226),  and  place  one  hand  on  the  conductor  of  a  machine.  Let 
the  other  open  hand  press  against  a  plate  of  glass  or  a  disk  of  vul- 
canite, held  on  the  open  hand  of  a  second  person  standing  on  the 
floor.  After  a  few  turns  of  the  machine,  let  the  hand  that  has  been 
on  the  prime  conductor  grasp  the  free  hand  of  the  second  person. 
Quite  a  shock  will  be  felt  by  both. 

It  is  evident  that  by  this  process  an  unusual  quantity 
of  electricity  had  collected  previous  to  the  discharge. 
The  explanation  is  simple.  The  hand  of  the  first  person, 
charged  with  +  E,  acts  by  induction  through  the  glass 
upon  the  second  person,  attracting  —  E  to  the  surface  of 
the  glass  with  which  his  hand  is  in  contact,  and  repelling 
+  E  to  the  earth.  Thus,  through  their  mutual  attraction, 
the  two  kinds  of  electricity  become,  as  it  were,  heaped  up 
opposite  each  other,  and  yet  are  prevented,  by  the  insu- 
lating glass,  from  uniting. 

211.  Leyden    Jar.  —  The   most   convenient   form   of 
condenser  is  the  Leyden  jar   (Fig.  208).     It  is  a  wide- 


ELECTRICAL   MACHINES. 


235 


Fig.  208. 


Fig.  2O9. 


mouthed  glass  jar  lined  on  the  inside  and  outside  for 
about  two-thirds  its  height  with  tin  foil.  Through  the 
stopper  passes  a  brass  rod  terminating  at  its  upper  ex- 
tremity in  a  brass  ball  #,  and  at  the  other  extremity  in 
a  brass  chain  which  touches  the  inner  coating  of  tin  foil. 

The  jar  may  be  charged 
by  connecting  one  of  its 
coatings  with  the  conductor 
of  an  electrical  machine,  and 
the  other  with  the  earth. 
Or  it  may  be  charged  by 
connecting  the  outside  coat- 
ing with  one  of  the  poles  of  the  Holtz  machine,  and 
bringing  the  other  pole  near  to  the  ball  leading  from  the 
inner  coating.  To  discharge  the  jar,  connect  the  outer 
coating  with  the  knob  of  the  jar.  To  avoid  a  shock  in  so 
doing  a  discharger  is  used  (Fig.  209),  which  consists  of  a 
bent  wire  terminating  at  each  end  with  metal  balls.  The 
wire  is  held  by  a  glass  insulating  handle. 

212.  Electrification  confined  to  the  External  Surface. 

Experiment  184.  —  Place  a  tin  fruit-can  on  a  clean,  dry  glass 
tumbler  (Fig.  210).  Fasten  a  circular  disk  a  of  tin  15mm  in  diameter 
to  one  end  of  a  rod  of  sealing-wax.  Charge  the  can  heavily 
with  electricity  from  an  electrical  machine.  Through  an 
orifice  c  in  the  can  introduce  the  disk,  and  touch  the  in- 
terior surface  of  the  can.  Withdraw  the  disk,  and  present 
it  to  an  electroscope.  It  shows  no  electrification.  Now 
touch  the  exterior  surface  of  the  can  with  the  disk  and 
present  it  tc  the  electroscope;  it  is  found  to  be  electrified.  Fjg.  210. 

This  experiment  shows  that  no  electricity  can  be  found 
inside  of  a  hollow  charged  conductor ;  or,  roughly  stated, 
a  static  charge  of  electricity  resides  on  the  exterior  surface 
of  a  conductor. 


236  ELECTRICITY   AND   MAGNETISM. 

213.  Effect  of  Points. —An  electrical  flyer,  F  (Fig.  206), 
consists  of   a  cap  of  metal  resting  upon  a  pointed  wire, 
which  serves   as   a   pivot.     The    cap   has   pointed   wires 
branching  out  from  it  like  the  spokes  of  a  wheel,  bent 
near  the  ends  and  turned  in  the  same  direction.     If  this 
is  placed  on  an  insulating  stand  and  connected  with  the 
conductor  of  an  electrical  machine  when  in  operation,  the 
air  particles  around  the  electrifying  points  become  excited 
like  so  many  pith-balls,  and  are  rapidly  repelled,  produc- 
ing a  continuous  current  of  air  issuing  from  the  points. 
The  reaction  of   these  air-particles  causes  the  wheel   to 
revolve  in  the  opposite   direction.     As  we  might  reason- 
ably expect,  currents  of  excited  air-particles  issuing  from 
the  points  on  an  excited  conductor  serve  to  carry  away 
with  them   portions  of   the  charge,  so  that  the  effect  of 
points  on  an  electrified  insulated  body  is  greatly  to  facilitate 
its  discharge. 

214.  Lightning.  —  Certain  clouds  which  have  formed  very  rapidly 
are  highly  charged  with  electricity,  usually  positively  charged.    The  sur- 
face of  the  earth  and  objects  thereon  immediately  beneath  the  cloud  are 
charged  inductively  with  the  opposite  kind  of  electricity.     The  cloud  and 
the  earth  correspond  to  the  coatings,  and  the  intervening  air  to  the  glass 
of  a  huge  Ley  den  jar.    The  charge  in  the  earth  and  that  in  the  cloud  hold 
each  other  prisoner  by  their  mutual  attraction,  until,  as  the  charges  accu- 
mulate, the   attraction   becomes   great  enough  to  disrupt  the  insulating 
medium,  i.e.  the  intervening  air,  when  a  discharge  takes  place.     It  is  the 
accumulation  of  induced  electricity  on  elevated  objects,  such  as  buildings 
and  trees,  that   offers   an   attraction  for  the  opposite  electricity  of  the 
cloud,  and  renders  them  especially  liable  to  be  struck  by  lightning. 

215.  Lightning-Rods.  —  The  flash  will  pass  along  the  line  of 
least  resistance.      A  good  lightning   conductor  offers  a  peaceful  means 
of  communication  between  the  earth  and  a  cloud  ;  it  leads  the  electricity  of 
the  earth  gently  up  toward  the  cloud,  and  allows  it  to  combine  with  its 
opposite  without  disturbance,  thereby  so  far  discharging  the  cloud  as  to 
prevent  a  lightning  stroke ;  or,  if  the  tension  is  too  great  to  be  thus  quietly 


ELECTRICAL  MACHINES.  237 

disposed  of,  the  flash  strikes  downward,  and  is  led  harmlessly  to  the  earth 
by  the  conductor.  An  ill-constructed  lightning-rod  may  be  worse  than  none. 
A  rod  should  be  made  of  good  conducting  material,  so  large  that  it  will 
not  be  melted,  and  free  from  loose  joints.  The  lower  end  should  be 
buried  in  earth  that  is  always  moist,  and  the  upper  end  should  terminate 
in  several  sharp  points. 


CHAPTER  VII. 

SOUND. 

Section  I. 

STUDY  OF   VIBRATIONS   AND   WAVES. 

The  subjects  of  Sound-waves  and  Light-waves,  which  we  are  about  to 
study,  have  two  important  characteristics  in  common  that  distinguish  them 
from  the  subjects  already  studied.  First,  each  of  them  affects  its  peculiar 
organ  of  sense,  the  ear  or  the  eye.  Secondly,  both  originate  in  vibrating 
bodies,  and  reach  us  only  by  the  intervention  of  some  medium  capable 
of  being  set  in  vibration. 

216.  Period  of  Vibration. 

Experiment  185.  —  Suspend  an  iron  ball  by  a  string,  as  in  Experi- 
ment 71,  cause  it  to  vibrate,  and,  watch  in  hand,  ascertain  the  num- 
ber of  vibrations  made  in  a  given  number  of  seconds ;  e.g.  60  seconds. 
Then,  remembering  that  all  the  vibrations  are  made  in  equal  intervals 
of  time,  ascertain  the  period  of  vibration  of  this  pendulum;  i.e.  the 
time  it  takes  to  make  each  vibration,  using  the  formula 

t=s-, 

n 

in  which  t  =  the  period,  and  n  =  the  number  of  vibrations  made  in  * 
seconds. 

217.  Direction  of  Vibration. 

Experiment  186.  —  Grasp  one  end  of  a  small  rod  or  yardstick  in 
a  vice,  pull  the  free  end  one  side,  and  set  it  in  vibration.  Pluck  a 
string  of  a  piano  or  violin.  Note  that  the  motions  of  all  the  bodies 
which  thus  far  we  have  caused  to  vibrate  are  at  right  angles  to  their 
length.  These  are  called  transverse  vibrations. 

Experiment  187.  —  Hang  up  a  spiral  spring  or  elastic  cord  with  a 
small  weight  attached  at  the  lower  end ;  lift  the  weight,  and,  drop- 


STUDY  OF   VIBRATIONS   AND   WAVES.  239 

ping  it,  notice  that  the  cord  vibrates  lengthwise.  This  is  a  case  of 
longitudinal  vibration.  There  may  also  be  torsional  vibrations,  for  ex- 
ample children  often  amuse  themselves  by  producing  these  by  twist- 
ing a  window  cord  and  tassel. 

218.  Propagation  of  Vibration ;  Waves. 

Experiment  188.  —  Take  a  rubber  cord  about  the  size  of  an  ordi- 
nary lead-pencil  and  12  feet  long.  Attach  at  intervals  a  few  glass 
beads  and  fasten  one  end  of  the  cord  to  the  wall  of  the  room.  Hold 
the  free  end  in  the  hand  and  draw  the  cord  out  so  as  to  be  nearly 
horizontal.  By  quick  movements  of  the  hand  in  a  horizontal  or  a 
vertical  direction  set  this  end  in  vibration.  Notice  that  these  vibra- 
tions are  communicated  from  point  to  point  along  the  cord,  and  that 
each  point  in  the  cord  successively  goes  through  a  vibration  precisely 
similar  to  that  held  in  the  hand.  Fix  the  eyes  upon  any  one  of  the 
beads ;  it  simply  vibrates  transversely.  Observe  the  cord  as  a  whole  ; 
waves  traverse  it  from  end  to  end,  but  it  is  easy  to  see  that  it  is  only 
a  form  that  traverses  it ;  the  beads  and  all  other  points  of  the  cord 
move  transversely.  These  successive  transverse  movements  give  rise 
to  the  wave-line  into  which  the  cord  is  thrown. 

219.  Wave-Length  and  Amplitude.  —  Imagine  an  in- 
stantaneous photograph  taken  of  the  cord  along  which  con- 
tinuous waves  are  passing.  It 

would  appear  much  like  the 

curved  line  CD  (Fig.  211).   c 

This   curved   line  represents 

what  is   known  as   a  simple  rig.  an. 

wave-line.     The  distance  from  any  vibrating  point  to  the 

nearest  point  which  is   in  exactly  the  same  stage  of  its 

vibration  is  called  a  wave-length^  as  wx,  uv,  or  en. 

The  distance  between  the  extreme  positions  of  a  vibrat- 
ing point  or  the  length  of  its  journey  is  called  the  ampli- 
tude of  the  wave  or  the  amplitude  of  vibration. 

2  2O.    Reflection  of  Waves  ;  Interference. 

Experiment  189.  — Stretch  the  cord  horizontally  between  two 


240 


SOUND. 


elevated  points,  and  pluck  it  with  the  hand  or  strike  it  with  a  stick 
near  one  end,  and  send  along  it  a  single  pulse,  forming  a  crest  on  the 

rope  (A,  Fig.  212).  This 
travels  to  the  other  end, 
and  there  we  see  it  re- 
flected and  inverted  (B). 
Experiment  190.  — 
Just  at  the  instant  of  re- 
flection, start  a  second 
crest ;  these  two,  the  crest 
and  the  returning  inverted 
crest  or  trough  (C),  are 
now  travelling  along  the  rope  in  opposite  directions,  and  must  meet 
at  some  point.  This  point  will  be  urged  upward  by  the  crest  and 
downward  by  the  trough,  and  so  its  motion  will  be  due  to  the  differ- 
ence of  the  two  forces. 

Experiment  191.  —  Send  along  the  rope,  first  a  trough,  then  a 
crest ;  now  two  crests  (D)  will  meet  near  the  middle  of  the  rope,  and 
the  motion  here  will  be  due  to  two  forces  acting  in  the  same  direc- 
tion, so  that  the  resulting  crest  will  be  greater  than  either  of  the  origi- 
nal ones. 

This  action  on  a  single  point  of  two  pulses,  or  two  trains 
of  waves,  no  matter  if  from  different  sources,  is  termed 
interference.  The  resulting  motion  may  be  greater  or  less 
than  that  due  to  either  pulse  alone,  or  it  may  be  zero. 

221.    Stationary  Vibrations,  Nodes,  etc. 

Experiment  192.  —  Hold  one  end  of  the  cord  while  the  other  is 
fixed,  and  send  along  it  a  regular  succession  of  equal  pulses  from  the 


Fig.  313. 

vibrating  hand;  it  will  be  easy,  by  varying  the  tension  and  rate  a 
little,  to  obtain  a  succession  of  hazy  spindles  (Fig.  213),  separated  by 
points  that  are  nearly  or  quite  at  rest,  Unlike  the  earlier  experiments, 


STUDY   OF   VIBRATIONS    AND    WAVES.  241 

the  waves  here  do  not  appear  to  travel  along  the  tube ;  yet  in  reality 
they  do  traverse  it.  The  deception  is  caused  by  stationary  points  being 
produced  by  the  interference  of  the  advancing  and  retreating  waves. 

This  interference  of  direct  and  reflected  waves  gives 
rise  to  the  important  class  of  so-called  stationary  vibrations. 
The  points  of  least  motion,  as  a  and  6,  are  called  nodes  ; 
the  points  of  greatest  motion,  c  and  c?,  are  called  antinodes  ; 
and  the  portion  of  the  rope  between  two  nodes,  as  ab,  is 
a  ventral  segment. 

222.    Longitudinal  Waves. 

Experiment  193.  —  Figure  214  represents  a  brass  wire  wound  in 
the  form  of  a  spiral  spring,  about  12  feet  long.  Attach  one  end  to  a 
cigar-box,  and  fasten  the  box  to  a  table.  Hold  the  other  end  H  of 
the  spiral  firmly  in  one  hand,  and  with  the  other  hand  insert  a  knife- 
blade  between  the  turns  of  the  wire,  and  quickly  rake  it  for  a  short 
distance  along  the  spiral  toward  the  box,  thereby  crowding  closer 
together  for  a  little  distance  (B)  the  turns  of  wire  in  front  of  the 
hand,  and  leaving 
the  turns  behind 
pulled  wider  apart 
(A)  for  about  an 

equal  distance.  The  Fis- 

crowded  part  of  the  spiral  may  be  called  a  condensation,  and  the 
stretched  part  a  rarefaction.  The  condensation,  followed  by  the  rare- 
faction, runs  with  great  velocity  through  the  spiral,  strikes  the 
box,  producing  a  sharp  thump;  is  reflected  from  the  box  to  the 
hand,  and  from  the  hand  again  to  the  box,  producing  a  second 
thump;  and  by  skilful  manipulation  three  or  four  thumps  will  be 
produced  in  rapid  succession.  If  a  piece  of  twine  be  tied  to  some 
turn  of  the  wire,  it  will  be  seen,  as  each  wave  passes  it,  to  receive  a 
slight  jerking  movement  forward  and  backward  in  the  direction  of 
the  length  of  the  spiral. 

How  is  energy  transmitted  through  the  spring  so  as  to 
deliver  the  blow  on  the  box  ?  Certainly  not  by  a  bodily 
movement  of  the  spiral  as  a  whole,  as  might  be  the  case  if 
it  were  a  rigid  rod.  The  movement  of  the  twine  shows 


242  SOUND. 

that  the  only  motion  which  the  coil  undergoes  is  a  vibra- 
tory movement  of  its  turns.  Here,  as  in  the  case  of 
water-waves,  energy  is  transmitted  through  a  medium  by 
the  transmission  of  vibrations. 

There  are  two  important  distinctions  between  these 
waves  and  those  which  we  have  previously  studied :  the 
former  consist  of  condensations  and  rarefactions;  the 
latter,  of  elevations  and  depressions.  In  the  former,  the 
vibration  of  the  parts  is  in  the  same  line  with  the  path 
of  the  wave,  and  hence  these  are  called  longitudinal  waves  ; 
in  the  latter,  the  vibration  is  across  its  path ;  they  are 
therefore  called  transverse  waves. 

A  wave  cannot  be  transmitted  through  an  inelastic  soft 
iron  spiral.  Elasticity  is  essential  in  a  medium,  that  it  may 
transmit  waves  composed  of  condensations  and  rarefactions  ; 
and  the  greater  the  elasticity,  the  greater  the  facility  and 
rapidity  with  which  a  medium  transmits  waves. 

223.  Air  as  a  Medium  of  Wave-Motion.  —  May  not 

air  and  other  gases,  which  are  elastic,  serve  as  media  for 
waves  ? 


Fig.  215. 

Experiment  194.  —  Place  a  candle  flame  at  the  orifice  a  of  the 
tube  (Fig.  215),  and  strike  the  table  a  sharp  blow  with  a  book  near 
the  orifice  b.  Instantly  the  candle  flame  is  quenched.  The  body  of 
air  in  the  tube  serves  as  a  medium  for  transmission  of  motion  to  the 
candle. 

Was  it  the  motion  of  a  current  of  air  through  the  tube,  a  minia- 


STUDY  OF   VIBRATIONS   AND  WAVES.  243 

ture  wind,  or  was  it  the  transfer  of  a  vibratory  motion  ?  Burn  touch- 
paper1  at  the  orifice  b,  so  as  to  fill  this  end  of  the  tube  with  smoke, 
and  repeat  the  last  experiment. 

Evidently,  if  the  body  of  the  air  is  moved  along  through  the  tube, 
the  smoke  will  be  carried  along  with  it.  The  candle  is  blown  out  as 
before,  but  no  smoke  issues  from  the  orifice  a.  It  is  clear  that  there  is  no 
translation  of  material  particles  from  one  end  to  the  other,  —  nothing 
like  the  flight  of  a  rifle  bullet.  The  candle  flame  was  struck  by  some- 
thing like  a  pulse  of  air,  not  by  a  wind. 

224.  How  a  Wave  is  propagated  through  a  Medium. 

—  The  effect  of  applying  force  with  the  hand  to  the  spiral 
spring  is  to  produce  in  a  certain  section  (B,  Fig.  214)  of 
the  spiral  a  crowding  together  of  the  turns  of  wire,  and 
at  A  a  separation ;  but  the  elasticity  of  the  spiral  instantly 
causes  B  to  expand,  the  effect  of  which  is  to  produce  a 
crowding  together  of  the  turns  of  wire  in  front  of  it,  in 
the  section  C,  and  thus  a  forward  movement  of  the  con- 
densation is  made.  At  the  same  time,  the  expansion  of  B 
causes  a  filling  up  of  the  rarefaction  at  A,  so  that  this 
section  is  restored  to  its  normal  state.  This  is  not  all : 
the  folds  in  the  section  B  do  not  stop  in  their  swing  when 
they  have  recovered  their  original  position,  but,  like  a 
pendulum,  swing  beyond  the  position  of  rest,  thus  produc- 
ing a  rarefaction  at  B,  where  immediately  before  there 
was  a  condensation.  Thus  a  forward  movement  of  the 
rarefaction  is  made,  and  thus  a  pulse  or  wave  is  trans- 
mitted with  uniform  velocity  through  a  spiral  spring,  air, 
or  any  elastic  medium. 

225.  Graphical  Method  of  Studying  Vihrations. 

Experiment  195.  —  Attach,  by  means  of  sealing-wax,  a  bristle  or 
a  fine  wire  to  the  end  of  one  of  the  prongs  of  a  large  steel  fork  (like 

1  To  prepare  touch-paper,  dissolve  about  a  teaspoonful  of  saltpetre  in  a  half-teacupful 
of  hot  water,  dip  unsized  paper  in  the  solution,  and  then  allow  it  to  dry.  The  paper 
produces  much  smoke  in  burning,  but  no  flame. 


244  SOUND. 

a  tuning-fork,  but  larger)  called  a  diapason.     Set  the  fork  in  vibra- 
tion, and  quickly  draw  the  point  of  the  bristle  lightly  over  a  smoked 

glass  (A,  Fig.  216).  A 
beautiful  wavy  line  will  be 
traced  on  the  glass,  each 

Fig.  216.  °  . 

wave    corresponding   to   a 
vibration  of  the  prong  when  vibrating  as  a  whole. 

Next,  tap  the  fork,  near  its  stem,  on  the  edge  of  a  table,  and  trace 
its  vibrations  on  a  smoked  glass  as  before.  You  will  generate  a 
similar  set  of  waves,  but,  running  over  these,  is  another  set,  of  much 
shorter  period,  like  No.  3  of  Figure  230,  showing  that  the  prong 
vibrates,  not  only  as  a  whole,  but  in  parts.  The  serrated  wavy  line 
produced  represents  the  resultant  of  the  combined  vibrations,  and 
may  be  called  a  complex  wave-line. 

QUESTIONS. 

1.  In  what  kind  of  motion  does  all  wave-motion  originate  ? 

2.  Watch  the  waves  of  the  ocean  moving  landward;  what  is  it 
that  advances? 

3.  Throw   a  cord   into  wavy  motion   by  the   movement  of  your 
hand ;  upon  what  do  the  number  and  the  length  of  the  waves  which 
traverse  the  cord  at  any  given  time  depend? 

4.  How  is  a  node  produced  ? 

5.  How  do  the  vibrations  in  longitudinal  waves  differ  from  the 
vibrations  in  transverse  waves? 

6.  Are  the  vibrations  in  air-waves  longitudinal  or  transverse  ? 


Section  II. 

SOUND-WAVES. 

226.  How  Sound-waves  Originate.  —  Listen  to  a 
sounding  church-bell.  It  produces  a  sensation ;  it  is 
heard.  The  ear  is  the  organ  through  which  the  sensation 


SOUND-WAVES.  245 

of  hearing  is  produced.  The  bell  is  at  such  a  distance 
that  it  cannot  act  directly  on  the  ear;  yet  something 
must  act  on  the  ear,  and  it  must  be  the  bell  which  causes 
that  something  to  act. 

Commencing  at  the  origin  of  sound,  let  the  first  in- 
quiry be,  How  does  a  sounding  body  differ  from  a  silent 
body? 

Experiment  196.  —  Strike  a  bell  or  a  glass  bell-jar,  and  touch  the 
edge  with  a  small  cork  ball  suspended  by  a  thread ;  you  not  only  hear 
the  sound,  but,  at  the  same  time,  you  see  a  tremulous  motion  of  the 
ball,  caused  by  a  motion  of  the  bell.  Touch  the  bell  gently  with  a 
finger,  and  you  feel  a  tremulous  motion.  Press  the  hand  against  the 
bell ;  you  stop  its  vibratory  motion,  and  at  that  instant  the  sound 
ceases.  Strike  the  prongs  of  a  tuning-fork,  press  the  stem  against  a 
table  :  you  hear  a  sound.  Thrust  the  ends  of  the  prongs  just  beneath 
the  surface  of  water ;  the  water  is  thrown  off  in  a  fine  spray  on  either 
side  of  the  vibrating  fork.  Watch  the  strings  of  a  piano,  guitar,  or 
violin,  or  the  tongue  of  a  jews-harp,  when  sounding.  You  can  see  that 
they  are  in  motion. 

Sound-waves  originate  in  a  vibrating  body. 

227.  How  Sound-waves  Travel.  —  How  can  a  bell, 
sounding  at  a  distance,  affect  the  ear?  If  the  bell  while 
sounding  possesses  no  peculiar  property  except  motion, 
then  it  has  nothing  to  communicate  to  the  ear  but  motion. 
But  motion  can  be  communicated  by  one  body  to  another 
at  a  distance  only  through  some  medium. 

Do  sound-waves  require  a  medium  for  their  communi- 
cation ? 

Experiment  197.  —  Lay  a  thick  tuft  of  cotton-wool  on  the  plate 
of  an  air-pump,  and  on  this,  face  downward,  place  a  loud-ticking 
watch,  and  cover  with  the  receiver.  Notice  that  the  receiver,  inter- 
posed between  the  watch  and  your  ear,  greatly  diminishes  the  sound, 
or  interferes  with  the  passage  of  something  to  the  ear.  Take  a  few 
strokes  of  the  pump  and  listen ;  the  sound  is  more  feeble,  and  con- 


246  SOUND. 

tinues  to  grow  less  and  less  distinct  as  the  exhaustion  progresses, 
until  either  no  sound  can  be  heard  when  the  ear  is  placed  close  to  the 
receiver,  or  an  extremely  faint  one,  as  if  coming  from  a  great  dis- 
tance. The  removal  of  air  from  a  portion  of  the  space  between  the 
watch  and  your  ear  destroys  the  sound.  Let  in  the  air  again,  and  the 
sound  is  restored. 

Sound-waves  cannot  travel  through  a  vacuum^  i.e.  with- 
out a  medium. 

Boys  often  amuse  themselves  by  inflating  paper  bags, 
and  with  a  quick  blow  bursting  them,  producing  with 
each  a  single  loud  report.  First  the  air  is  suddenly  and 
greatly  condensed  by  the  blow,  and  the  bag  is  burst ;  the 
air  now,  as  suddenly  and  with  equal  force,  expands,  and 
by  its  expansion  condenses  the  air  for  a  certain  distance 
all  around  it,  leaving  a  rarefaction  where  just  before  had 
been  a  condensation.  If  many  bags  were  burst  at  the 
same  spot  in  rapid  succession,  the  result  would  be  that 
alternating  shells  of  condensation  and  rarefaction  would 
be  thrown  off,  all  having  a  common  center,  enlarging  as 
they  advance,  like  the  waves  formed  by  stones  dropped 
into  water ;  except  that,  in  this  case,  the  waves  are  not 
like  rings,  but  hollow  globes ;  not  circular,  but  spherical. 
In  this  manner  sound-waves  produced  by  the  vibration 
of  a  sounding  body  travel  through  the  air. 

As  a  wave  advances,  each  individual  air-particle  con- 
cerned in  its  transmission  performs  a  short  excursion  to 
and  fro  in  the  direction  of  a  straight  line  radiating  from 
the  center  of  the  shells  or  hollow  globes.  A  sound-wave 
travels  its  own  length  in  the  time  that  a  particle  occupies 
in  going  through  one  complete  vibration  so  as  to  be  ready 
to  start  again. 

Experiment  198.  —  Take  a  strip  of  black  cardboard  4.5  inches  X 
1  inch.  Cut  a  slit  about  one-sixteenth  of  an  inch  wide  lengthwise 
and  centrally  through  the  strip  nearly,  from  end  to  end.  Place  the 


SOUND-WAVES. 


247 


slit  over  the  dotted  line  at  the  bottom  of  Figure  217,  and  draw  the 
book  along  underneath  in  the  direction  of  the  arrow.  Imagine  that 
the  short  white  dashes  seen  through  the  slit  represent  a  series  of  air- 
particles,  and  the  slit  itself  represents  the  direction  in  which  a  series 
of  sound-waves  are  travelling.  It  will  be  seen  that  each  air-particle 
moves  a  little  to  and  fro  in  the  direction  in  which  the  sound  travels 
and  comes  back  to  its  starting-point ;  but  the  condensations  and  rare- 
factions, represented  by  a  group  (half  a  wave-length)  of  dots  being 
alternately  closer  together  or  farther  apart,  are  transmitted  through 
the  whole  series  of  air-particles. 


Fig.  217. 

228.  What   Sound   Is. — Sound  is  a  sensation  caused 
usually  by  waves  of  air  beating  upon  the  organ  of  hearing. 

229.  Solids  and  Liquids   as  Media  for  transmitting 
Sound-waves. 

Experiment  199.  —  Lay  a  watch,  with  its  back  downward,  on  a 


248  SOUND. 

long  board  (or  table),  near  to  one  of  its  ends,  and  cover  the  watch 
with  loose  folds  of  cloth  till  its  ticking  cannot  be  heard  through  the 
air  in  any  direction  at  a  distance  equal  to  the  length  of  the  board. 
Now  place  the  ear  in  contact  with  the  farther  end  of  the  board,  and 
you  will  hear  the  ticking  of  the  watch  very  distinctly. 

Experiment  200.  —  Place  one  end  of  a  long  pole  on  a  cigar  box, 
and  apply  the  stem  of  a  vibrating  diapason  to  the  other  end;  the 
sound-vibrations  will  be  transmitted  through  the  pole  to  the  box,  and 
a  loud  sound  will  be  given  out  by  the  box,  as  though  that,  and  not  the 
tuning-fork,  were  the  origin  of  the  sound. 

Experiment  201. — Place  the  ear  to  the  earth,  and  listen  to  the 
rumbling  of  a  distant  carriage ;  or  put  the  ear  to  one  end  of  a  long 
stick  of  timber,  and  let  some  one  gently  scratch  the  other  end  with  a 
pin. 

Solids  and  liquids,  as  well  as  gases,  transmit  sound- 
vibrations. 


Section  III. 

VELOCITY  OF   SOUND-WAVES. 

23O.  The  Velocity  of  Sound-waves  depends  on  the 
Elasticity  and  Density  of  the  Medium.  —  The  relation 
of  velocity  to  the  density  and  elasticity  of  gases,  as  ascer- 
tained by  careful  experiment,  is  as  follows:  the  velocity 
of  sound-waves  in  gases  is  directly  proportional  to  the  square 
root  of  their  elasticity,  and  inversely  proportional  to  the 
square  root  of  their  respective  densities. 

The  velocity  of  sound-waves  in  air  at  0°C.  is  (333m) 
1093  feet  per  second.  The  velocity  increases  nearly  two 
feet  for  each  degree  centigrade.  At  the  temperature  of 
16°  C.  (60°  F.)  we  may  reckon  the  velocity  of  sound-waves 
at  about  (342m)  1125  feet  per  second. 


REFLECTION  OF  SOUND-WAVES.  —  ECHOES.          249 

The  greater  density  of  solids  and  liquids,  as  compared 
with  gases,  tends,  of  course,  to  diminish  the  velocity  of 
sound-waves ;  but  their  greater  incompressibility  more 
than  compensates  for  the  decrease  of  velocity  occasioned 
by  the  increase  of  density.  As  a  general  rule,  solids  are 
more  incompressible  than  liquids;  hence,  sound-waves 
generally  travel  faster  in  the  former  than  in  the  latter. 
For  example,  sound-waves  travel  in  water  about  4  times 
as  fast  as  in  air,  and  in  iron  and  glass  16  times  as  fast. 


Section  IV. 

REFLECTION   OF   SOUND-WAVES.  —  ECHOES. 

f 

231.  Reflection.  —  In  the  experiment  with  the  spiral 
spring,  waves  were  reflected  from  the  box  to  the  hand,  and 
from  the  hand  to  the  box.  When  a  sound-wave  meets  an 
obstacle  in  its  course,  it  is  reflected;  and  the  sound  re- 
sulting from  the  reflected  waves  is  often  called  an  echo, 
or,  when  they  are  many  times  reflected  so  that  the  sound 

becomes  nearly  contin- 

J 
uous,  a  reverberation. 


232.  Sound-waves 
reflected  by  Concave 
Mirrors. 

Experiment  202  .—Place 
a  watch  at  the  focus  A  (Fig.  Fig'  818' 

218)  of  a  concave  mirror  G.  At  the  focus  B  of  another  concave 
mirror  H,  place  the  large  opening  of  a  small  tunnel,  and  with  a 
rubber  connector  attach  the  bent  glass  tube  C  to  the  nose  of  the 


250  SOUND. 

tunnel.  The  extremity  D  being  placed  in  the  ear,  the  ticking  of  the 
watch  can  be  heard  very  distinctly,  as  though  it  were  somewhere  near 
the  mirror  H.  Though  the  mirrors  be  12  feet  apart,  the  sound  will 
be  louder  at  B  than  at  an  intermediate  point  E. 

How  is  this  explained  ?  Every  air-particle  in  a  certain 
radial  line,  as  Ac,  receives  and  transmits  motion  in  the 
direction  of  this  line  ;  the  last  particle  strikes  the  mirror 
at  <?,  and  being  perfectly  elastic,  bounds  off  in  the  direc- 
tion cc',  communicating  its  motion  to  the  particles  in  this 
line.  At  c'  a  similar  reflection  gives  motion  to  the  air 
particles  in  the  line  c'B.  In  consequence  of  these  two  re- 
flections, all  divergent  lines  of  motion  as  Ac?,  Ae,  etc.,  that 
meet  the  mirror  G,  are  there  rendered  parallel,  and  after- 
wards rendered  convergent  at  the  mirror  H.  The  prac- 
tical result  of  the  concentration  of  this  scattering  energy 
is,  that  a  sound  of  great  intensity  is  heard  at  B.  The 
points  A  and  B  are  called  the  foci  of  the  mirrors.  The 
front  of  the  wave  as  it  leaves  A  is  convex,  in  passing 
from  G  to  H  it  is  plane,  and  from  H  to  B  concave.  If 
you  fill  a  large  circular  tin  basin  with  water,  and  strike 
one  edge  with  a  knuckle,  circular  waves  with  concave 
fronts  will  close  in  on  the  centre,  heaping  up  the  water 
at  that  point. 

Long  "  whispering-galleries "  have  been  constructed  on  this  principle. 
Persons  stationed  at  the  foci  of  the  concave  ends  of  the  long  gallery  can 
carry  on  a  conversation  in  a  whisper  which  persons  between  cannot  hear. 

The  external  ear  is  a  wave-condenser.  The  hand  held  concave  behind 
the  ear,  by  its  increased  surface,  adds  to  its  efficiency.  An  ear-trumpet, 
by  successive  reflections,  serves  to  concentrate,  at  the  small  orifice  open- 
ing into  the  ear,  the  sound-waves  that  enter  at  the  large  end. 


INTENSITY  OF  SOUND.  251 

Section  V. 

INTENSITY   OF   SOUND. 

233.  Intensity  depends  on  the  Amplitude  of  Vibra- 
tion.—  Gently  tap  the  prongs  of  a  tuning-fork   and  dip 
them  into  water,  —  the  water  is  scarcely  moved  by  them ; 
increase  the  force  of  the  blow,  —  the   vibrations  become 
wider,  and  the  water  spray  is  thrown  with  greater  force 
and  to  a  greater  distance.    The  same  thing  occurs  when  the 
fork  vibrates  in  the  air ;  though  we  do  not  see  the  air-par- 
ticles as  they  are  batted  by  the  moving  fork,  yet  we  feel  the 
effects  as  a  sound  sensation,  and  we  judge  of  their  energy 
by  the   intensity  of  the   sensation   which   they   produce. 
Loudness  of  sound  refers  to  the  intensity  of  a  sensation. 
We  have  no  standard  of  measurement  for  a  sensation,  so 
we  are  compelled  to  measure  the  intensity  of  the  sound- 
wave, knowing  at  the  same  time  that  loudness  is  not  pro- 
portional to  this  intensity.     Unfortunately,  the  expressions 
loudness    and    intensity    of   sound-wave    are    often   inter- 
changed.    The   intensity  of  a  vibration  is  measured  by 
the  energy  of  the  vibrating  particle.     It  is  clear  that  if 
the  amplitude  of  vibration  of  a  particle  is  doubled  while 
its  period  remains  constant,  its  velocity  is  doubled,  and 
its  energy  is   increased  fourfold.     Hence,  (1)  measured 
mechanically,  the  intensity  of  a  sound-wave  is  proportional 
to  the    square   of  the    amplitude  of  the   vibrations  of  the 
vibrating  body. 

234.  Intensity  depends  upon  the  Density  of  the  Me- 
dium.—  In  the  experiment   with   the   watch   under   the 
receiver  of  the   air-pump    (page   245),  the   sound  grew 


252  SOUND. 

feebler  as  the  air  became  rarer.  Aeronauts  are  obliged  to 
exert  themselves  more  to  make  their  conversation  heard 
when  they  reach  great  hights  than  when  in  the  denser 
lower  air.  (2)  The  intensity  of  sound-waves  increases  with 
the  density  of  the  medium  in  which  they  are  produced. 

235.  Intensity  depends  on   Distance.  —  It  is  a  mat- 
ter of  every-day  observation  that  the  loudness  of  a  sound 
diminishes  very  rapidly  as  the  distance  from  the  source 
of  the  waves  to  the  ear  increases.     As  a  sound-wave  ad- 
vances  in   an   ever-widening   sphere,  a  given  amount  of 
energy  becomes  distributed  over  an  ever-increasing  sur- 
face ;  and  as  a  greater  number  of  particles  partake  of  the 
motion,  the  individual   particles   receive  proportionately 
less  energy ;  hence  it  follows,  —  as  a  consequence  of  the 
geometrical  truth,  that  "  the  surface  of  a  sphere  varies 
as  the  square  of  its  radius,"  —  that  (3)  the  intensity  of 
a  sound-wave  varies  inversely  as  the  square  of  the  distance 
from  its  source.     For  example,  if  two  persons,  A  and  B, 
are  respectively  500  and  1000  rods  from  a  gun  when  it 
is  discharged,  the  waves  that  reach  A  will  be  four  times 
as  intense  as  the  same  when  they  reach  B. 

236.  Speaking-Tubes. 

Experiment  203.  —  Place  a  watch  at  one  end  of  the  long  tin  tube 
(Fig.  215),  and  the  ear  at  the  other  end.  The  ticking  sounds  very 
loud,  as  though  the  watch  were  close  to  the  ear. 

Long  tin  tubes,  called  speaking-tubes,  passing  through  many  apartments 
in  a  building,  enable  persons  at  the  distant  extremities  to  carry  on  conver- 
sation in  a  low  tone  of  voice,  while  persons  in  the  various  rooms  through 
which  the  tube  passes  hear  nothing.  The  reason  is  that  the  sound-waves 
which  enter  the  tube  are  prevented  from  expanding,  consequently  the 
intensity  of  sound  is  not  affected  by  distance,  except  as  its  energy  is  wasted 
by  friction  of  the  air  against  the  sides  of  the  tube. 


EEENFOECEMENT   OF  SOUND-WAVES. 


253 


Section  VI. 

EEENFOBCEMENT    OF    SOUND-WAVES    AND   INTERFERENCE 
OF   SOUND-WAVES. 

237.  Reenforcement  of  Sound-waves. 

Experiment  204.  —  Set  a  diapason  in  vibration ;  you  can  scarcely 
hear  the  sound  unless  it  is  held  near  the  ear.  Press  the  stem  against 
a  table ;  the  sound  rings  out  loud,  but  the  waves  seem  to  proceed 
from  the  table. 

When  only  the  fork  vibrates,  the  prongs  presenting 
little  surface  cut  their  way  through  the  air,  producing  very 
slight  condensations,  and  consequently  waves  of  little  in- 
tensity. When  the  fork  rests  upon  the  table,  the  vibrations 
are  communicated  to  the  table ;  the  table  with  its  larger 
surface  throws  a  larger  mass  of  air  into  vibration,  and 
thus  greatly  intensifies  the  sound-waves.  The  strings  of 
the  piano,  guitar,  and  violin 
owe  as  much  of  their  loud- 
ness  of  sound  to  their  elas- 
tic sounding-boards,  as  the 
fork  does  to  the  table. 

238.  Reinforcement  by 
Bodies    of    Air ;     Resona- 
tors. 

Experiment  205.  —  Take  a 
glass  tube  A  (Fig.  219),  16  inches 
long  and  2  inches  in  diameter; 
thrust  one  end  into  a  vessel  of 
water  C,  and  hold  over  the  other 

end  a  vibrating  diapason  B  that  makes  (say)  256  vibrations   in  a 
second.    Gradually  lower  the  tube  into  the  water,  and  when  it  reaches 


254  SOUND. 

a  certain  depth,  i.e.  when  the  column  of  air  oc  attains  a  certain  length, 
the  sound  of  the  fork  becomes  very  loud;  continuing  to  lower  the 
tube,  the  sound  rapidly  dies  away. 

Columns  of  air  are  thus  found  to  serve,  as  well  as  sound- 
ing-boards, to  reenforce  sound-waves.  The  instruments 
which  enclose  the  columns  of  air  are  called  resonators. 
Unlike  sounding-boards,  they  can  respond  loudly  to  only 
one  tone,  or  to  a  few  tones  of  widely  different  pitch. 

How  is  this  reinforcement  effected  ?  When  the  prong 
a  moves  from  one  extremity  of  its  arc  a'  to  the  other  a", 
it  sends  a  condensation  down  the  tube ;  this  condensation 
striking  the  surface  of  the  water,  is  reflected  by  it  up  the 
tube.  Now  suppose  that  the  front  of  this  reflected  con- 
densation should  just  reach  the  prong  at  the  instant  it  is 
starting  on  its  retreat  from  an  to  a' ;  then  the  reflected 
condensation  will  conspire  with  the  condensation  formed  by 
the  prong  in  its  retreat  to  make  a  greater  condensation  in 
the  air  outside  the  tube.  Again,  the  retreat  of  the  prong 
from  arr  to  af  produces  in  its  rear  a  rarefaction,  which  also 
runs  down  the  tube,  is  reflected,  and  will  reach  the  prong 
at  the  instant  it  is  about  to  return  from  ar  to  a",  and  to 
cause  a  rarefaction  in  its  rear;  these  two  rarefactions 
moving  in  the  same  direction  conspire  to  produce  an  in- 
tensified rarefaction.  The  original  sound-waves  thus  com- 
bine with  the  reflected,  to  produce  resonance  ;  but  this  can 
only  happen  when  the  like  parts  of  each  wave  coincide 
each  with  each ;  for  if  the  tube  were  somewhat  longer  or 
shorter  than  it  is,  it  is  plain  that  condensations  would 
meet  rarefactions  in  the  tube,  and  tend  to  destroy  one 
another. 

The  loudness  of  sound  of  all  wind  instruments  is  due  to  the  resonance 
of  the  air  contained  within  them.  A  simple  vibratory  movement  at  the 
mouth  or  orifice  of  the  instrument,  scarcely  audible  in  itself,  such  as  the 


REENFORCEMENT  OF   SOUND-WAVES. 


255 


vibration  of  a  reed  in  reed  pipes,  or  a  pulsatory  movement  of  the  air  pro- 
duced by  the  passage  of  a  thin  sheet  of  air  over  a  sharp  wooden  or  metallic 
edge,  as  in  organ  pipes,  flutes,  and  flageolets,  or  more  simply  still  by  the 
friction  of  a  gentle  stream  of  breath  from  the  lips  sent  obliquely  across 
the  open  end  of  a  closed  tube,  bottle,  or  pen-case,  is  sufficient  to  set  the 
large  body  of  enclosed  air  in  the  instrument  into  vibration,  and  thus  re- 
enforced,  the  sound  becomes  audible  at  long  distances. 

Experiment  206.  —  Attach  a  rose  gas-burner  A  (Fig.  220)  to  a 
metal  gas-tube  about  lm  in  length,  and  connect  this  by  a  rubber  tube 
with  a  gas-burner.  Light  the  gas  at  the  rose  burner, 
and  you  will  hear  a  low,  rustling  noise.  Remove  the 
conical  cap  from  the  long  tin  tube  (Fig.  215),  support 
the  tube  in  a  vertical  position,  and  gradually  raise  the 
burner  into  the  tube ;  when  it  reaches  a  certain  point 
not  far  up,  the  body  of  air  in  the  tube  will  catch  up 
the  vibrations,  and  give  out  deafening  sound-waves 
that  will  shake  the  walls  and  furniture  in  the  room. 

239.  Measuring  Wave-Lengths  and  the 
Velocity  of  Sound-waves.  —  Experiments 
like  that  described  on  page  253  enable  us  read- 
ily to  measure  the  wave-length  produced  by  a 
fork  that  makes  a  given  number  of  vibrations 
in  a  second,  and  also  to  measure  the  velocity 
of  sound-waves.  It  is  evident  that  if  a  con-  Fig.  220. 
densation  generated  by  the  prong  of  the  fork  in  which  its 
forward  movement  from  a'  to  a"  (Fig.  220)  met  with  no 
obstacle,  its  front,  meantime,  would  traverse  the  distance 
od,  or  twice  the  distance  oc\  hence  the  length  of  the 
condensation  is  the  distance  od.  But  a  condensation  is 
only  one-half  of  a  wave,  and  the  passage  of  the  prong 
from  af  to  a"  is  only  one-half  of  a  vibration ;  conse- 
quently the  distance  od  is  one-half  of  a  wave-length,  and 
the  distance  oc  is  one-fourth  of  a  wave-length.  The 
measured  distance  of  oc  in  this  case  is  about  13.13  inches ; 
hence  the  length  of  wave  produced  by  a  C'-fork  making 


256 


SOUND. 


256  vibrations  in  a  second  is  (13.13  inches  X  4  =•)  52.5 
inches  =  4.38  feet.  And  since  a  wave  from  this  fork 
travels  4.38  feet  in  -g-i-g-  of  a  second,  it  will  travel  in  an 
entire  second  (4.38  feet  X  256  =)  1121  feet.  The  dis- 
tance oc  varies  with  the  temperature  of  the  air. 

It  is  evident  that  the  three  quantities  expressed  in  the 
formula 

i       ,1  velocity 

wave-length  = r 7 — rr — -: 

number  01  vibrations 

bear  such  a  relation  to  one  another  that  if  any  two  are 
known,  the  remaining  quantity  can  be  computed.  It 
will  further  be  observed  that  with  a  given  velocity  the  wave- 
length varies  inversely  as  the  number  of  vibrations  ;  i.e.  the 
greater  the  number  of  vibrations  per  second,  the  shorter 
the  wave-length. 

24O.   Interference  of  Sound- Waves. 

Experiment  207.  —  Hold  a  vibrating  diapason  over  a  resonance- 
jar  as  in  Figure  221.  Roll  the 
diapason  over  slowly  in  the  fin- 
gers. At  certain  points,  a  quarter 
of  a  revolution  apart,  when  the 
diapason  is  in  an  oblique  posi- 
tion with  reference  to  the  edge 
of  the  jar  as  represented  in  the 
figure,  the  reenforcement  from 
the  tube  almost  entirely  dis- 
appears, but  reappears  at  the 
intermediate  points.  Return  to 
the  position  where  there  is  no 
resonance,  and  enclose  in  a  loose 
roll  of  paper,  the  prong  farthest 
from  the  tube,  without  touching  the  diapason,  so  as  to  prevent  the 
sound-waves  produced  by  that  prong  from  passing  into  the  tube ;  the 
resonance  resulting  from  the  vibrations  of  the  other  prong  immediately 
appears. 


Fig.  221. 


REENFOKCEMENT   OF   SOUND-WAVES. 


257 


Experiment  208.  —  Select  two  of  the  tubes  (Fig.  235)  of  nearly 
the  same  length,  blow  through  them,  and  notice  the  peculiar  throbbing 
sound  produced  by  the  interference  of  the  two  sounds. 

Experiment  209.  —  Stop  one  of  the  orifices  of  a 
bicyclist's  whistle  (Fig.  222),  and  sound  one  whistle  at  a 
time.  The  sound  of  each  is  clear  and  smooth.  Sound 
both  whistles  at  the  same  time,  and  you  obtain  the  usual 
rough  and  discordant  sound. 

The  two  whistles  of  unequal  length  give  out  waves  of 
slightly  different  length,  so  that  at  certain  short  inter- 
vals the  same  phases  of  both  sets  will  coincide  (i.e.  con- 
densation with  condensation)  and  produce  intensified 
sounds  which  are  heard  at  long  distances,  while  at  other 
intervals  opposite  phases  coincide  (i.e.  condensation  with 
rarefaction),  and  the  result  of  their  mutual  destruction 
is  to  cause  the  otherwise  smooth  sound  to  become  broken 
or  rattling. 


***' 


Two  sound-waves  may  unite  to  produce  a  sound  louder  or 
weaker  than  either  alone  would  produce,  or  even  cause  silence. 

241.    Forced  and  Sympathetic  Vibrations. 

Experiment  210.  —  Suspend  from  a  frame  several  pendulums,  A, 

B,  C,  etc.  (Fig.  223).    A  and  D  are  each  3  feet  long,  C  a  little  longer, 
and  B  and  E  are  shorter.     Set  A  in  vibration,  and  slight  impulses 
will  be  communicated  through  the  frame  to 

D  and  cause  it  to  vibrate.  The  vibration- 
period  of  D  being  the  same  as  that  of  A, 
all  the  impulses  tend  to  accumulate  motion 
in  D,  so  that  it  soon  vibrates  through  arcs 
as  large  as  those  of  A.  On  the  other  hand, 

C,  B,  and  E,  having  different  rates  of  vibra- 
tion from  that  of  A,  will  at  first  acquire  a 
slight  motion,  but  soon  their  vibrations  will 
be  in  opposition  to  those  of  A,  and  then  the 
impulses  received  from  A  will  tend  to  destroy 
the  slight  motion  they  had  previously  acquired. 

Experiment  211.  —  Press  down  gently  one  of  the  keys  of  a  piano 
so  as  to  raise  the  damper  without  making  any  sound,  and  then  sing 


258  SOUND. 

loudly  into  the  instrument  the  corresponding  note.  The  string  cor- 
responding to  this  note  will  be  thrown  into  vibrations  that  can  be 
heard  for  several  seconds  after  the  voice  ceases.  If  another  note  be 
sung,  this  string  will  respond  only  feebly. 

Raise  the  dampers  from  all  the  strings  of  the  piano  by  pressing  the 
foot  on  the  right-hand  pedal,  and  sing  strongly  some  note  into  the 
piano.  Although  all  the  strings  are  free  to  vibrate,  only  those  will 
respond  loudly  that  correspond  to  the  note  you  sing,  i.e.  those  that  are 
capable  of  making  the  same  number  of  vibrations  per  second  as  are 
produced  by  your  voice. 

These  experiments  show  that  a  vibrating  body  tends  to 
make  other  bodies  near  it  vibrate  even  if  their  periods  of 
vibrations  are  different.  Vibrations  of  this  kind,  such,  for 
example,  as  those  of  B,  C,  and  E  in  Experiment  210  and 
those  generated  in  the  sounding-boards  of  pianos,  violins, 
etc.,  are  called  forced  vibrations.  But  if  the  period  of  the 
incident  waves  of  air  is  the  same  as  that  of  the  body  which 
they  cause  to  vibrate,  the  amplitude  and  intensity  of  the 
vibrations  become  very  great,  like  that  of  the  pendulum  D, 
and  those  of  the  piano  strings  which  gave  forth  the  loud 
sounds.  Such  are  called  sympathetic  vibrations. 

QUESTIONS. 

1.  Why  do  not  sound-waves  travel  with  the  same  velocity  through 
all  bodies? 

2.  How  are  echoes  produced  ? 

3.  On  a  day  when  sound-waves  travel  through  the  air  at  the  rate  of 
1120  feet  per  second,  what  is  the  length  of  the  sound-waves  that  pro- 
ceed from  a  church  bell  which  makes  192  vibrations  in  a  second? 

4.  With  what  velocity  do  sound-waves  travel  when  a  jar  whose 
depth  is  10  inches  gives  the  maximum  reenforcement  for  a  diapason 
which  makes  256  vibrations  in  a  second? 

5.  Great   danger  often  arises  from  vibrations  of  the  walls  of  a 
building  caused  by  certain  vibratory  movements  of  machinery  within. 
The  danger  in  such  cases  can  frequently  be  greatly  diminished  by 
changing  the  rate  of  motion  in  the  machinery.     Explain. 


PITCH  OF  MUSICAL  SOUNDS.  259 

Section  VII. 

PITCH   OF   MUSICAL  SOUNDS. 

242.  On  What  Pitch  Depends. 

Experiment  212.  —  Draw  the  finger-nail  or  a  card  slowly,  and 
then  rapidly,  across  the  teeth  of  a  comb.  The  two  sounds  produced 
are  commonly  described  as  low  or  grave,  and  high  or  acute.  The  hight 
of  a  musical  sound  is  its  pitch. 

Experiment  213.  —  Cause  the  circular  sheet-iron  disk  A  (Fig.  224) 
to  rotate,  and  hold  a  corner  of  a  visiting-card  so  that  at  each  hole  an 
audible  tap  shall  be  made.  Notice  that  when 
the  separate  taps  or  noises  cease  to  be  distin- 
guishable, the  sound  becomes  musical;  also, 
that  the  pitch  of  the  musical  sound  depends 
upon  the  rapidity  of  the  rotation,  i.e.  upon  the 
frequency  of  the  taps. 

Experiment  214.  —  Hold  the  orifice  of  a 
glass  tube  B  so  as  to  blow  through  the  holes  as 
they  pass.  When  rotating  slowly,  separate  puffs 
are  heard,  from  which  it  hardly  seems  possible 
to  construct  a  musical  sound.  When,  however,  Flg*  a34* 

the  ear  is  no  longer  able  to  detect  the  separate  puffs,  the  sound  be- 
comes quite  musical,  and  the  pitch  rises  and  falls  with  the  speed. 

Pitch  depends  upon  frequency  of  vibration,  or  wave- 
length; i.e.  the  greater  the  number  of  vibrations  per  second, 
or  the  shorter  the  wave-length,  the  higher  the  pitch. 

243.  Musical  Scale.  —  The  pitch  of  a  sound  produced 
by  twice  as  many  vibrations  as  that  of  another  sound  is 
called  the  octave  of  the  latter.     Between  two  such  sounds 
the  voice  rises  or  falls  in  a  manner  very  pleasing  to  the 
ear  by  a  definite  number  of  steps.     This  gives  rise  to  the 


260 


SOUND. 


so-called  musical  scale,  or  gamut.     The  number  of  vibra- 


J 

Vibration 
numbers.  1 

Vibration  1 
ratios. 

c 

132 

1 

D 

148£ 

1 

E 

165 

5 

F 

176 

4 

G 

198 

3 

A 

220 

4 

B 

247  J 

¥ 

C' 

264 

2 

D' 

297 

E' 

330 

| 

F' 

352 

f 

G' 

396 

| 

A' 
B' 

C" 

440 
495 

528 

f 

Fig.  335. 

piano   makes 


tions  which  shall  constitute  a  given  note 
is  purely  arbitrary,  and  differs  slightly 
in  different  countries  ;  but  the  ratios 
between  the  vibration  numbers  of  the 
several  notes  of  the  gamut  and  the 
vibration  number  of  the  first  or  funda- 
mental note  of  the  gamut,  are  the  same 
among  all  enlightened  nations.  The 
vibration  numbers  given  in  Figure  225 
correspond  to  those  of  German  instru- 
ments. For  example,  the  string  corre- 
sponding to  the  middle  C  (the  key  at 
the  left  of  the  two  black  keys  near  the 
middle  of  the  key-board)  of  a  German 
264  vibrations  in  a  second. 


Section  VIII. 

VIBRATION   OF    STRINGS. 

244.    Sonometer. 

Experiment  215.  —  Stretch   an  elastic  wire  a   over  the  bridges 
of  the  sonometer  (Fig.  226),  so  that  the  portion  between  will  be  free 


Fig.  336. 

to  vibrate.  Pluck  the  string  at  its  middle  with  the  thumb  and  finger, 
causing  it  to  vibrate,  and  observe  the  pitch.  Next  place  a  movable 
bridge  d  half-way  between  the  two  fixed  bridges  and  cause  the  portion 


VIBRATION   OF   STRINGS.  261 

between  either  fixed  bridge  and  the  movable  bridge  to  vibrate,  and 
observe  the  change  in  pitch.  How  is  the  vibration  period  changed? 

Experiment  216.  —  Stretch  another  wire  b,  either  thicker  or  thin- 
ner than  the  last,  employing  the  same  length  and  tension  as  before, 
and  notice  the  change  in  pitch  due  to  the  difference  of  weight  of 
the  wire.  How  is  the  vibration  period  changed? 

Experiment  217.  —  Increase  the  tension  of  either  wire  by  turning 
the  pin,  to  which  one  end  of  the  wire  is  attached,  with  a  wrench  C, 
and  observe  the  change  in  pitch  caused  by  change  of  tension.  How 
does  an  increase  of  tension  affect  the  vibration  period? 

Careful  experiments  show  that  the  vibration  numbers  of 
strings  of  the  same  material  vary  inversely  as  their  lengths 
and  the  square  roots  of  their  weights,  and  directly  as  the 
square  roots  of  their  tension. 

245.   Beats. 

Experiment  218. —  Strike  simultaneously  the  lowest  note  of  a 
piano  and  its  sharp  (black  key  next  above) ,  and  listen  to  the  result- 
ing sound. 

You  hear  a  peculiar  wavy  or  throbbing  sound,  caused 
by  an  alternate  rising  and  sinking  in  loudness.  These 
alternations  in  loudness  are  called  beats. 


Fig.  227. 

Let  the  continuous  curve  line  AC  (Fig.  227)  represent  a 
series  of  waves  caused  by  striking  the  lower  key,  and  the 
dotted  line  a  series  of  waves  proceeding  from  the  upper 
key.  Now  the  waves  from  both  keys  may  start  together 
at  A ;  but  as  the  waves  from  the  lower  key  are  given  less 


262  SOUND. 

frequently,  so  are  they  correspondingly  longer ;  and  at 
certain  intervals,  as  at  B,  condensations  will  correspond 
with  rarefactions,  producing  by  their  interference  momen- 
tary silence,  too  short,  however,  to  be  perceived ;  but  the 
sound  as  perceived  by  the  ear  is  correctly  represented  in 
its  varying  loudness  by  the  curved  line  in  the  lower  part 
of  the  figure. 

The  number  of  beats  per  second  due  to  two  simple  tones  is 
equal  to  the  difference  of  their  respective  vibration  numbers. 
The  sensation  produced  on  the  ear  by  such  a  throbbing 
sound,  when  the  beats  are  sufficiently  frequent,  is  un- 
pleasant, much  as  the  sensation  produced  by  flashes  of 
light  that  enter  the  eye,  when  you  walk  on  the  shady 
side  of  a  picket  fence,  is  unpleasant.  The  unpleasant 
sensation,  called  by  musicians  discord,  is  due  to  beats. 


Section  IX. 

OVEBTONES   AND   HARMONICS. 

246.    Vibration  in  Parts. 

Experiment  219.  —  Hang  up  a  rubber  cord  AC  (Fig.  228)  4  feet 
long,  and  fasten  both  ends.  Pluck  it  near  the  middle,  and  it  will 
swing  to  and  fro  as  a  whole  (2),  at  a  rate  dependent  on  its  length, 
tension,  etc.  Hold  it  fast  at  B  (3),  and  pluck  it  at  a  point  half-way 
between  A  and  B.  Both  halves  are  thrown  into  independent  vibra- 
tions, and  continue  so  to  vibrate  for  a  brief  time  after  the  hand  is 
withdrawn  from  B.  Again  hold  it  fast  at  B,  one-third  its  length 
above  A  (4),  and  pluck  it  half-way  between  A  and  B ;  the  length  BC 
instantly  divides  itself  at  B'  into  two  equal  parts,  and  on  withdraw- 
ing the  hand  from  B,  the  whole  cord  is  seen  to  vibrate  in  three  dis- 
tinct and  equal  sections.  In  a  similar  manner  it  may  be  made  to 
vibrate  in  four,  five,  etc.,  sections. 


OVERTONES    AND    HARMONICS.  263 

Sounds  coming  from  a  string  or  other  body  that  vibrates 
in  parts  are  called  overtones.  If,  as  is  the  case  with  a 
string,  the  vibration  num- 
ber of  the  overtone  is 
just  two,  three,  four,  etc., 
times  that  of  the  funda- 
mental or  lowest  tone, 
the  sound  is  called  a  har- 
monic. Many  overtones 
can  be  produced  from  a 
steel  bar  or  a  metallic 
plate,  but  no  harmonics. 
This  distinction  is  of 
great  importance,  for, 
practically,  no  musical 
instruments  are  of  much 
use  unless  their  vibrat- 
ing parts  furnish  harmon- 
ics. Fig.  238. 

Experiment  220.  —  Press  down  the  C'-key  (middle  C)  of  a  piano 
gently,  so  that  it  will  not  sound ;  and  while  holding  it  down,  strike 
the  C-wire  strongly.  In  a  few  seconds  release  the  key,  so  that  its 
damper  will  stop  the  vibrations  of  the  string  that  was  struck,  and 
you  will  hear  a  sound  which  you  will  recognize  by  its  pitch  as  com- 
ing from  the  C'-wire.  Place  your  finger  lightly  on  the  C'-wire,  and 
you  will  find  that  it  is  indeed  vibrating.  Press  down  the  right  pedal 
with  the  foot,  so  as  to  lift  the  dampers  from  all  the  wires,  strike  the 
C-key,  and  touch  with  the  finger  the  C'-wire ;  it  vibrates.  Touch  the 
keys  next  to  C',  viz.  B  and  D' ;  they  have  only  a  slight  forced  vibra- 
tion. Touch  G' ;  it  vibrates. 

Now  it  is  evident  that  the  vibrations  of  the  C7  and  G'- 
wires  are  sympathetic.  A  C-wire  vibrating  as  a  whole 
cannot  cause  sympathetic  vibrations  in  a  C'-wire ;  but  if 
it  vibrates  in  halves,  it  may.  Hence  we  conclude  that 


264  SOUND. 

when  the  C-wire  was  struck,  it  vibrated,  not  only  as  a 
whole,  giving  a  sound  of  its  own  pitch,  but  also  in  halves ; 
and  the  result  of  this  latter  set  of  vibrations  was,  that  an 
additional  sound  was  produced  by  this  wire,  just  an  octave 
higher  than  the  first-mentioned  sound. 

Again,  the  G'-wire  makes  three  times  as  many  vibra- 
tions as  are  made  by  the  C-wire ;  hence  the  latter  wire, 
in  addition  to  its  vibrations  as  a  whole  and  in  halves,  must 
have  vibrated  in  thirds,  inasmuch  as  it  caused  the  G'-wire 
to  vibrate.  It  thus  appears  that  a  string  may  vibrate  at 
the  same  time  as  a  whole,  in  halves,  thirds,  etc.,  and  the 
result  is  that  a  sound  is  produced  that  is  compounded  of 
several  sounds  of  different  pitch. 

Not  only  do  stringed  instruments  produce  compound 
tones,  but  no  ordinary  musical  instrument  is  capable  of 
producing  a  simple  tone,  i.e.  a  sound  generated  by  vibra- 
tions of  a  single  period.  In  other  words,  when  any  note  of 
any  musical  instrument  is  sounded,  there  is  produced,  in 
addition  to  the  primary  tone,  a  number  of  other  tones  in  a 
progressive  series,  each  tone  of  the  series  being  usually  of 
less  intensity  than  the  preceding.  The  primary  or  lowest 
tone  of  a  note  is  usually  sufficiently  intense  to  be  the  most 
prominent,  and  hence  is  called  the  fundamental  tone. 

That  two  notes  sounded  together  may  harmonizet  it  is 
essential  not  only  that  the  pitch  of  their  fundamental  tones 
be  so  widely  different  that  they  cannot  produce  audible  beats, 
but  that  no  beat  shall  be  formed  by  their  overtones,  or  by  an 
overtone  and  a  fundamental.  Not  only  is  there  perfect 
agreement  among  the  overtones  of  two  notes  an  octave 
apart  when  sounded  together,  as  when  male  and  female 
voices  unite  in  singing  the  same  part  of  a  melody,  but 
the  richness  and  vivacity  of  the  sound  is  much  increased 
thereby. 


QUALITY   OF   SOUND.  265 

Section  X. 

QUALITY   OF   SOUND. 

247.  How  Sounds  from  Different  Sources  are  Distin- 
guished. —  We  easily  learn  to  distinguish  by  certain  pecu- 
liarities the  voices  of  our  acquaintances.     So  we  readily 
distinguish  sounds  emanating  from  various  musical  instru- 
ments, e.g.  a   piano,  violin,  harp,  and  cornet.     It  is   not 
necessarily  by  the  loudness  or  pitch  of  the  sounds  that  we 
recognize  them.    It  is  by  another  property  of  sound  called 
quality.       Two  sounds  can  differ  from  each  other  in   only 
three  particulars,  viz.  intensity,  pitch,  and  quality. 

Pitch  depends  on  frequency  of  vibrations,  loudness  on 
their  amplitude ;  on  what  does  quality  depend  ? 

248.  Analysis  of  Sounds.  —  The  unaided  ear  is  unable, 
except   to   a   very  limited 

extent,  to  distinguish  the 
individual  tones  that  com- 
pose a  note.  Helmholtz  ar- 
ranged a  series  of  resona- 
tors consisting  of  hollow 
spheres  of  brass,  each  hav- 
ing two  openings :  one  (A, 
Fig.  229)  large,  for  the  re- 
ception of  the  sound-waves,  rig.  239. 
and  the  other  (B)  small  and  funnel-shaped,  and  adapted 
for  insertion  into  the  ear.  Each  resonator  of  the  series 
was  adapted  by  its  size  to  resound  powerfully  to  only  a 
single  tone  of  a  definite  pitch.  When  any  musical  sound 
is  produced  in  front  of  these  resonators,  the  ear,  placed  at 
the  orifice  of  any  one,  is  able  to  single  out  from  a  collec- 
tion that  overtone,  if  present,  to  which  alone  this  resonator 


266 


SOUND. 


is  capable  of  responding.  In  this  manner  a  complete 
analysis  of  any  musical  sound  may  be  made,  and  the  pitch 
and  intensity  of  each  of  its  components  determined. 

It  is  found  that  when  a  note  is  produced  on  a  given  instrument,  not 
only  is  there  a  great  variety  of  intensity  represented  by  the  overtones,  but 
all  the  possible  overtones  of  the  series  are  by  no  means  present.  Which 
are  wanting  depends  very  much,  in  stringed  instruments,  upon  the  point  of 
the  string  struck.  For  example,  if  a  string  is  struck  in  its  middle,  no  node 
can  be  formed  at  that  point ;  consequently,  the  two  important  overtones 
produced  by  2  and  4  times  the  number  of  vibrations  of  the  fundamental 
will  be  wanting.  Strings  of  pianos,  violins,  etc.,  are  generally  struck  near 
one  of  their  ends,  and  thus  they  are  deprived  of  only  some  of  their  higher 
and  feebler  overtones. 

249.  Synthesis  of  Sounds.  —  The  sound  of  a  tuning- 
fork,  when  its  fundamental  is  reenforced  by  a  suitable 
resonance-cavity,  is  very  nearly  a  simple  tone.  By  sound- 
ing simultaneously  several  forks  of  different  but  appropri- 
ate pitch,  and  with  the  requisite  relative  intensities,  Helm- 
holtz  succeeded  in  producing  sounds  peculiar  to  various 
musical  instruments,  and  even  in  imitating  most  of  the 
vowel  sounds  of  the  human  voice. 


Fig.  230. 

Thus  it  appears  that  he  has  been  able  to  determine, 
both  analytically  and  synthetically,  that  the  quality  of  a 
given  sound  depends  upon  what  overtones  combine  with  its 
fundamental  tone,  and  on  their  relative  intensities  ;  or,  we 
may  say  more  briefly,  upon  the  form  of  vibration,  since  the 
form  must  be  determined  by  the  character  of  its  components. 


COMPOSITION   OF   SONOROUS    VIBRATIONS. 


267 


Section  XI. 

COMPOSITION  OF  SONOROUS   VIBRATIONS,   AND  THE 
RESULTANT   WAVE-FORMS. 

25O.  Method  of  Representing-  Sound- Vibrations 
Graphically.  —  It  is  evident  that  there  must  be  a'  particular  aerial 
wave-form  corresponding  to  each  compound  vibration,  otherwise  the  ear 
would  not  be  able  to  appreciate  a  difference  in  the  quality  of  sounds  to 
which  these  combination  forms  give  rise.  Every  particle  of  air  engaged  in 


Fig.  831. 


Fig.  332. 

transmitting  a  compound  sound-wave  is  simultaneously  acted  upon  by 
several  sets  of  vibratory  movements,  and  it  remains  to  investigate  what 
its  motion  will  be  under  their  joint  influence. 

The  light  wave-lines  AB  (Fig,  230)  represent  typically  two  series  of 


268 


SOUND. 


aerial  sound-waves,  corresponding  respectively  to  a  fundamental  tone  and  its 
first  overtone.  The  heavy  line  represents  the  form  of  the  joint  wave  which 
results  from  the  combination  of  the  two  constituents.  If  we  suppose  lines 
perpendicular  to  the  axis,  that  is,  to  the  dotted  line,  or  line  of  repose,  to 
be  drawn  to  each  point  in  this  line,  as  ab,  cd,  eF,  etc.,  they  will  represent 
by  their  varying  lengths  the  displacement  of  any  particle  in  a  vibrating 
body,  or  any  particle  of  air  traversed  by  sound-waves,  from  its  normal 
position. 

The  rectangular  dia- 
gram CD  is  intended 
to  represent  a  portion 
of  a  transverse  section 
of  a  body  of  air  trav- 
ersed by  the  joint  wave 
represented  by  the 
heavy  wave-line  above. 
The  depth  of  shading 
in  different  parts  in- 
dicates the  degree  of 
condensation  at  those 
parts. 

Figure  231  repre- 
sents wave-lines  drawn 
by  an  instrument  call- 
ed a  vibrograph  (Fig. 
232).  The  second  line 
represents  a  sound  two 
octaves  above  that 
which  the  first  line  rep- 
resents, and  the  third 
line  shows  the  result  of 
the  combination  of  the 
Fig.  833.  two  setg  Of  vibrations. 

251.  Manometric  Flames. —Apparatus  like  that  shown  in 
Figure  233  will  serve  to  illustrate  in  a  pleasing  manner  many  facts  per- 
taining to  sound  vibrations. 

The  cylindrical  box  A  is  divided  by  a  membrane  a  into  two  compart- 
ments c  and  6.  Illuminating-gas  is  introduced  into  the  compartment  c, 
through  the  rubber  tube  n,  and  burned  at  the  orifice  d.  CD  is  a  frame 
holding  two  mirrors,  M,  placed  back  to  back,  so  that  whichever  side  is 
turned  toward  the  flame  there  is  a  reflection  of  the  flame. 


COMPOSITION  OF   SONOROUS   VIBRATIONS. 


269 


When  the  mirror  is  at  rest,  an  image  of  the  flame  will  appear  in  the 
mirror  as  represented  by  A  (Fig.  234).  If  the  mirror  is  rotated,  the 
flame  appears  drawn  out  in  a  band  of  light,  as  shown  in  B  of  the  same 
figure. 


Fig.  334. 

Sing  into  the  cone  B  (Fig.  234)  the  sound  of  oo  in  tool,  and  waves  of 
air  will  run  down  the  tube,  beat  against  the  membrane  a,  causing  it  to 
vibrate,  and  the  membrane  in  turn  acts  upon  the  gas  in  the  compartment  c, 
throwing  it  into  vibration.  The  result  is,  that  instead  of  a  flame  appear- 
ing in  the  rotating  mirror  as  a  continuous  band  of  light,  as  B,  Figure  234, 


270  SOUND.       - 

it  is  divided  up  into  a  series  of  tongues  of  light,  as  shown  in  C,  each  con- 
densation being  represented  by  a  tongue,  and  each  rarefaction  by  a  dark 
interval  between  the  tongues.  If  a  note  an  octave  higher  than  the  last  is 
sung,  we  obtain,  as  we  should  expect,  twice  as  many  tongues  in  the  same 
space,  as  shown  in  D.  E  represents  the  result  when  the  two  tones  are 
produced  simultaneously,  and  illustrates  in  a  striking  manner  the  effect  of 
interference.  F  represents  the  result  when  the  vowel  e  is  sung  on  the  key 
of  C' ;  and  G,  when  the  vowel  o  is  sung  on  the  same  key.  These  are  called 
manometric  flames. 


Section  XII. 

MUSICAL   INSTRUMENTS. 

252.  Classification  of  Musical  Instruments.  —  Musi- 
cal instruments  may  be  grouped  into  three  classes :  (1) 
stringed  instruments;    (2)    wind  instruments,  in  which 
the  sound  is  due  to  the  vibration  of  columns  of  air  con- 
fined  in   tubes;    (3)  instruments   in  which  the  vibrator 
is  a  membrane  or  plate.     The  first  class  has  received  its 
share  of  attention ;  the  other  two  merit  a  little  further 
consideration. 

253.  Wind  Instruments. 

Experiment  221.  —  Figure  235  represents  a  set  of  Quinke's 
whistles.  The  tubes  are  of  the  same  size,  but  of  varying  length. 
Blow  through  the  small  tube  across  the  lips  of  the  large  tube  of  each 
whistle  in  the  order  of  their  lengths,  commencing  with  the  longest. 

Repeat  the  experiment,  closing  the  end  of  the  whistle  farthest 
from  you  with  a  finger,  so  as  to  make  what  is  called  a  "  closed  pipe." 

The  pitch  of  vibrating  air-columns,  as  well  as  of  strings, 
varies  with  the  length,  and  in  both  stopped  and  open  pipes 


MUSICAL  INSTRUMENTS. 


271 


the  number  of  vibrations  is  inversely  proportional  to  the 
length  of  the  pipe.  An  open  pipe  gives  a  note  an  octave 
higher  than  a  closed  pipe  of  the  same  length. 


Fig.  235. 

Experiment  222.  —  Take  some  of  the  longer  whistles,  blow  as 
before,  gradually  increasing  the  force  of  the  current.  It  will  be  found 
that  only  the  gentle  current  will  give  the  full  musical  fundamental 
tone  of  the  tube,  —  a  little  stronger  current  produces  a  mere  rustling 
sound ;  but  when  the  force  of  the  current  reaches  a  certain  limit,  an 
overtone  will  break  forth ;  and,  on  increasing  still  further  the  power 
of  the  current,  a  still  higher  overtone  may  be  reached. 

Figure  236  represents  an  open  organ -pipe  provided  with  a  glass 
window  A  in  one  of  its  sides.  A  wire  hoop  B  has  stretched  over  it  a 
membrane,  and  the  whole  is  suspended  by  a  thread  within  the  pipe.  If 
the  membrane  is  placed  near  the  upper  end,  a  buzzing  sound  proceeds 


272 


SOUND. 


from  the  membrane  when  the  fundamental  tone  of  the  pipe  is  sounded ; 
and  sand  placed  on  the  membrane  will  dance  up  and  down  in  a  lively 
manner.  On  lowering  the  membrane,  the  buzzing  sound  becomes 
fainter,  till,  at  the  middle  of  the  tube,  it  ceases  entirely,  and  the  sand 
becomes  quiet1.  Lowering  the  membrane  still  further,  the  sound  and 
dancing  recommence,  and  increase  as  the  lower  end  is  approached. 

When  the  fundamental  tone  of  an  open  pipe  is  produced, 
its  air-column  divides  itself  into  two  equal  vibrating  sections, 
with   the   anti-node   at  the  extremities   of  the 
tube,  and  a  node  in  the  center. 


Fig.  336. 

If  the  pipe  is  stopped,  there  is  a  node  at  the  stopped 
end ;  if  it  is  open,  there  is  an  anti-node  at  the  open 
end;  and  in  both  cases  there  is  an  anti-node  at  the  end 
where  the  wind  enters,  which  is  always  to  a  certain 
extent  open. 

A,  B,  and  C  of  Figure  237  show  respectively  the  posi- 
tions of  the  nodes  and  anti-nodes  for  the  fundamental  tone 


MUSICAL  INSTRUMENTS. 


273 


and  first  and  second  overtones  of  a  closed  pipe ;  and 
A',  B',  and  C'  show  the  positions  of  the  same  in  an 
open  pipe  of  the  same  length.  The  distance  between  the 
dotted  lines  shows  the  relative  amplitudes  of  the  vibra- 
tions of  the  air-particles  at  various  points  along  the  tube. 
Now  the  distance  between  a  node  and  the  nearest  anti- 
node  is  a  quarter  of  a  wave-length.  Comparing,  then, 
A  and  A',  it  will  be  seen  that  the  wave-length  of  the 
fundamental  of  the  closed  pipe  must  be  twice  the  wave- 
length of  the  fundamental  of  the  open  pipe :  hence  the 
vibration  period  of  the  latter  is  half  that  of  the  former ; 
consequently  the  fundamental  of  the  open  pipe  must  be 
an  octave  higher  than  that  of  the  closed  pipe. 


Fig.  338. 

254.    Sounding  Plates,  etc. 

Experiment  223.  —  Fasten  with  a  screw  the  elastic  brass  plate  A 
(Fig.  238)  on  the  upright  support.  Strew  writing-sand  over  the  plate, 
and  draw  a  rosined  bass  bow  steadily  and  firmly  over  one  of  its 
edges  near  a  corner ;  and  at  the  same  time  touch  the  middle  of  one 


274 


SOUND. 


of  its  edges  with  the  tip  of  the  finger;  a  musical  sound  will  be 
produced,  and  the  sand  will  dance  up  and  down,  and  quickly  collect 
in  two  rows,  extending  across  the  plate  at  right  angles  to  one  an- 
other. Draw  the  bow  across  the  middle  of  an  edge,  and  touch  with  a 
finger  one  of  its  corners  ;  the  sand  will  arrange  itself  in  two  diagonal 
rows  (2)  across  the  plate,  and  the  pitch  of  the  note  will  be  a  fifth 
higher.  Touch,  with  the  nails  of  the  thumb  and  forefinger,  two 
points  a  and  b  (3)  on  one  edge,  and  draw  the  bow  across  the  middle 
c  of  the  opposite  edge,  and  you  will  obtain  additional  rows  and  a 
shriller  note. 


Fig.  239. 

By  varying  the  position  of  the  point  touched  and  bowed, 
a  great  variety  of  patterns  can  be  obtained,  some  of  which 
are  represented  in  Figure  239.  It  will  be  seen  that  the 
effect  of  touching  the  plate  with  a  finger  is  to  prevent 
vibration  at  that  point,  and  consequently  a  node  is  there 
produced.  The  whole  plate  then  divides  i'tself  up  into 
segments  with  nodal  division  lines  in  conformity  with  the 


MUSICAL  INSTRUMENTS.  275 

node  just  formed.  The  sand  rolls  away  from  those  parts 
which  are  alternately  thrown  into  crests  and  troughs,  to 
the  parts  that  are  at  rest. 

255.  Interference. 

Experiment  224.  —  C  (Fig.  238)  is  a  tin  tube  made  in  two  parts  to 
telescope  one  within  the  other.  The  extremity  of  one  of  the  parts  ter- 
minates in  two  slightly  smaller  branches.  Bow  the  plate,  as  in  the  first 
experiment  (1),  place  the  two  orifices  of  the  branches  over  the  segments 
marked  with  the  +  signs,  and  regulate  the  length  of  the  tube  so  as  to 
reenforce  the  note  given  by  the  plate,  and  set  the  plate  in  vibration. 
Now  turn  the  tube  around,  so  that  one  orifice  may  be  over  a  +  seg- 
ment, and  the  other  over  a  —  segment ;  the  sound  due  to  resonance 
entirely  ceases.  It  thus  appears  that  the  two  segments  marked  -f 
pass  through  the  same  phases  together ;  likewise  the  phases  of  —  seg- 
ments correspond  with  one  another;  i.e.  when  one  +  segment  is 
bent  upward,  the  other  is  bent  upward,  and  at  the  same  time  the  two 
—  segments  are  bent  downward ;  for,  when  the  two  orifices  of  the 
tube  are  placed  over  two  +  segments  or  two  —  segments,  two  condensa- 
tions followed  by  two  rarefactions  pass  up  these  branches  and  unite 
at  their  junction  to  produce  a  loud  sound ;  but  when  one  of  the 
orifices  is  over  a  +  segment,  and  the  other  over  a  —  segment,  a  con- 
densation passes  up  one  branch  at  the  same  time  that  a  rarefaction 
passes  up  the  other,  and  the  two  destroy  one  another  when  they  come 
together;  i.e.  the  two  sound-waves  combine  to  produce  silence. 

256.  Bells.  —  A  bell  or  goblet  is  sub- 
ject to  the   same  laws  of  vibration  as  a 
plate. 

Experiment  225.  —  Nearly  fill  a  large  goblet 
with  water,  strew  upon  the  surface  lycopodium 
powder,  and  draw  a  rosined  bow  gently  across  the 
edge  of  the  glass.  The  surface  of  the  water  will 
become  rippled  with  wavelets  (Fig.  240)  radiating 
from  four  points  90°  apart,  corresponding  to  the 
centers  of  four  ventral  segments  into  which  the  Flg>  340' 

goblet  is  divided,  and  the  powder  will  collect  in  lines  proceeding  from 
the  nodal  points  of  the  bell.  By  touching  the  proper  points  of  a 


276 


SOUND. 


bell  or  glass  with  a  finger-nail,  it  may  be  made  to  divide  itself,  like  a 

plate,  into  6,  8,  10,  etc.  (always  an  even  number),  vibrating  parts. 
Experiment  226.  —  Remove  the  brass  plate  (Fig.  239)  from  its 

support,  and  fasten  the  bell  B  (Fig.  241)  on  the  support.     Bow  the 

edge  of  the  bell  at  some  point,  and 
hold  the  open  tube  C  in  a  horizon- 
tal position  with  the  center  of  one 
of  its  walls  near  that  point  of  the 
edge  of  the  bell  which  is  opposite 
the  point  bowed.  The  tube  loudly 
reenforces  the  sound  of  the  bell. 
Move  the  tube  around  the  edge  of 
Fig.  241.  the  bell  and  find  its  nodes. 

Thrust  the  plunger  D  into  the  open  end  E  of  the  tube,  and  find 

what  part  of  the  length  of  an  open  tube  a  closed  tube  should  be  to 

reenforce  a  sound  of  a  given  pitch. 

257.  Vocal  Organs.  —  It  is  difficult  to  say  which  is 
more  to  be  admired,  —  the  wonderful  capabilities  of  the 
human  voice  or  the  extreme  sim- 
plicity of  the  means  by  which  it  is 
produced.  The  organ  of  the  voice 
is  a  reed  instrument  situated  at  the 
top  of  the  windpipe,  or  trachea.  A 
pair  of  elastic  bands  aa  (Fig.  242), 
called  the  vocal  chords,  is  stretched 
across  the  top  of  the  windpipe.  The 
air-passage  £>,  between  these  chords, 
is  open  while  a  person  is  breathing ; 
Fig.  242.  kut  when  he  speaks  or  sings,  they 

are  brought  together  so  as  to  form  a  narrow,  slit-like 
opening,  thus  making  a  sort  of  double  reed,  which  vibrates 
when  air  is  forced  from  the  lungs  through  the  narrow 
passage,  somewhat  like  the  little  tongue  of  a  toy  trum- 
pet. The  sounds  are  grave  or  high  according  to  the 
tension  of  the  chords,  which  is  regulated  by  muscular 


SOME   SOUND-WAVE  RECEIVERS.  277 

action.  The  cavities  of  the  mouth  and  the  nasal  passages 
form  a  compound  resonance-tube.  This  tube  adapts  it- 
self, by  its  varying  width  and  length,  to  the  pitch  of  the 
note  produced  by  the  vocal  chords.  Place  a  finger  on 
the  protuberance  of  the  throat  called  "  Adam's  apple," 
and  sing  a  low  note ;  then  sing  a  high  note,  and  you  will 
observe  that  the  protuberance  rises  in  the  latter  case,  thus 
shortening  the  distance  between  the  vocal  chords  and  the 
lips.  Set  a  timing-fork  in  vibration,  open  the  mouth  as  if 
about  to  sing  the  corresponding  note,  place  the  fork  in 
front  of  it,  and  the  cavity  of  the  mouth  will  resound  to 
the  note  of  the  fork,  but  will  cease  to  do  so  when  the 
mouth  adapts  itself  to  the  production  of  some  other  note. 
The  different  qualities  of  the  different  vowel  sounds  are 
produced  by  the  varying  forms  of  the  resonating  mouth- 
cavity,  the  pitch  of  the  fundamental  tones  given  by  the 
vocal  chords  remaining  the  same.  This  constitutes  articu- 
lation. 


Section  XIII. 

SOME   SOUND-WAVE   RECEIVERS. 

258.  The  Phonograph.  —  Figure  243  represents  the  Edison 
phonograph.  A  metallic  cylinder  A  is  rotated  by  means  of  a  crank.  On 
the  surface  of  the  cylinder  is  cut  a  shallow  helical  groove  running  around 
the  cylinder  from  end  to  end,  like  the  thread  of  a  screw.  A  small  metallic 
point,  or  style,  projecting  from  the  under  side  of  a  thin  metallic  disk  D 
(Fig.  244),  which  closes  one  orifice  of  the  mouth-piece  B,  stands  directly 
over  the  thread.  By  a  simple  device  the  cylinder,  when  the  crank  is 
turned,  is  made  to  advance  just  rapidly  enough  to  allow  the  groove  to 
keep  constantly  under  the  style.  The  cylinder  is  covered  with  tinfoil. 
The  cone  F  is  usually  applied  to  the  mouth-piece  to  concentrate  the  sound- 
waves upon  the  disk  D. 


278 


SOUND. 


Now,  when  a  person  directs  his  voice  toward  the  mouth-piece,  the  aerial 
waves  cause  the  disk  D  to  participate  in  every  motion  made  by  the  parti- 
cles of  air  as  they  beat  against  it,  and  the  motion  of  the  disk  is  communi- 


Fig.  243. 

cated  by  the  style  to  the  tinfoil,  producing  thereon  impressions  or  indenta- 
tions as  it  passes  on  the  rotating  cylinder.  The  result  is  that  there  is  left 
upon  the  foil  an  exact  representation  in  relief  of  every  movement  made  by 
the  style.  Some  of  the  indentations  are  quite  perceptible  to  the  naked 
eye,  while  others  are  visible  only  with 
the  aid  of  a  microscope  of  high  power. 
Figure  245  represents  a  piece  of  the  foil 
as  it  would  appear  inverted  after  the  in- 
dentations (here  greatly  exaggerated) 
have  been  imprinted  upon  it.  Fig.  244. 

The  words  addressed  to  the  phonograph  having  been  thus  impressed 
upon  the  foil,  the  mouth-piece  and  style  are  temporarily  removed,  while 
the  cylinder  is  brought  back  to  the  position  it  had 
when  the  talking  began,  and  then  the  mouth-piece 
is  replaced.    Now,  evidently,  if  the  crank  is  turned 
Fig.  245.  jn  t^e  same  direction  as  before,  the  style,  resting 

upon  the  foil  beneath,  will  be  made  to  play  up  and  down  as  it  passes 
over  ridges  and  sinks  into  depressions ;  this  will  cause  the  disk  D  to 


I 
SOME   SOUND-WAVE   RECEIVERS. 


2T9 


reproduce  the  same  vibratory  movements  that  caused  the  ridges  and 
depressions  in  the  foil.  The  vibrations  of  the  disk  are  communicated 
to  the  air,  and  through  the  air  to  the  ear ;  thus  the  words  spoken  to  the 
apparatus  may  be,  as  it  were,  shaken  out  into  the  air  again  at  any  subse- 
quent time,  even  centuries  after,  accompanied  by  the  exact  accents,  into- 
nations, and  quality  of  sound  of  the  original. 

259.  The  Ear.  —  In  Figure  246,  A  represents  the  external  ear-passage; 
a  is  a  membrane,  called  the  tympanum,  stretched  across  the  bottom  of  the 
passage,  and  thus  closing  the  orifice  of  a  cavity  b,  called  the  drum  ;  c  is  a 


Fig.  246. 

chain  of  small  bones  stretching  across  the  drum,  and  connecting  the 
tympanum  with  the  thin  membranous  wall  of  the  vestibule  e ;  ff  are  a 
series  of  semicircular  canals  opening  into  the  vestibule;  g  is  the  open- 
ing into  another  canal  in  the  form  of  a  snail-shell  </,  hence  called  the 
cochlea  (this  is  drawn  on  a  reduced  scale)  ;  d  is  a  tube  (the  Eustachian 
tube}  connecting  the  drum  with  the  throat ;  and  h  is  the  auditory  nerve. 
The  vestibule  and  all  the  canals  opening  into  it  are  filled  with  a  trans- 
parent liquid.  The  drum  of  the  ear  contains  air,  and  the  Eustachian  tube 
forms  a  means  of  ingress  and  egress  for  air  through  the  throat. 

Now  how  does  the  ear  hear  ?  and  how  is  it  able  to  distinguish  between 
the  infinite  variety  of  form,  rapidity,  and  intensity  of  aerial  sound-waves 


280  SOUND. 

so  as  to  interpret  correctly  the  corresponding  quality,  pitch,  and  loudness 
of  sound  ?  Sound-waves  enter  the  external  ear-passage  A  as  ocean-waves 
enter  the  bays  of  the  seacoast,  are  reflected  inward,  and  strike  the  tym- 
panum. The  air-particles,  beating  against  this  drum-head,  impress  upon 
it  the  precise  wave -form  that  is  transmitted  to  it  through  the  air  from  the 
sounding  body.  The  motion  received  by  the  drum-head  is  transmitted 
by  the  chain  of  bones  to  the  membranous  wall  of  the  vestibule.  From 
the  walls  of  the  spiral  passage  of  the  cochlea  project  into  its  liquid  con- 
tents thousands  of  fine  elastic  threads  or  fibres,  called  "  rods  of  Corti." 
As  the  passage  becomes  smaller  and  smaller,  these  vibratile  rods  become 
of  gradually  diminishing  length  and  size  (such  as  the  wires  of  a  piano 
may  roughly  represent),  and  are  therefore  suited  to  respond  sympatheti- 
cally to  a  great  variety  of  vibration-periods.  This  arrangement  is  some- 
times likened  to  a  "  harp  of  three  thousand  strings "  (this  being  about 
the  number  of  rods).  The  auditory  nerve  at  this  extremity  is  divided 
into  a  large  number  of  filaments,  like  a  cord  unravelled  at  its  end,  and 
one  of  these  filaments  is  attached  to  each  rod.  Now,  as  the  sound- 
waves reach  the  membranous  wall  of  the  vestibule,  they  set  it,  and  by 
means  of  it  the  liquid  contents,  into  forced  vibration,  and  so  through  the 
liquid  all  the  fibres  receive  an  impulse.  Those  rods  whose  vibration 
periods  correspond  with  the  periods  of  the  constituents  forming  the  com- 
pound wave  are  thrown  into  sympathetic  vibration.  The  rods  stir  the 
nerve  filaments,  and  the  nerve  transmits  to  the  brain  the  impressions  re- 
ceived. Just  as  a  piano  when  its  dampers  are  raised  and  a  person  sings 
into  it,  may  be  said  to  analyze  each  sound-wave,  and  show  by  the  vibrat- 
ing strings  of  how  many  tones  it  is  composed,  as  well  as  their  respective 
pitch,  and  by  the  amplitude  of  their  vibrations  their  respective  intensi- 
ties ;  so,  it  is  thought,  this  wonderful  harp  of  the  ear  analyzes  every  com- 
plex sound-wave  into  a  series  of  simple  vibrations.  Tidings  of  the  dis- 
turbances are  communicated  to  the  brain,  and  there,  in  some  mysterious 
manner,  these  disturbances  are  interpreted  as  sound  of  definite  quality. 
pitcht  and  intensity. 


CHAPTER   VIII. 
RADIANT  ENERGY,   ETHER-WAVES,  — LIGHT. 

Section  I. 

INTRODUCTION. 

26O.  Energy  Received  from  the  Sun.  —  Exposed  to 
the  sun,  the  skin  is  warmed,  —  the  sense  of  touch  is 
affected;  it  is  illuminated,  —  thereby  the 
sense  of  sight  is  affected ;  it  is  tanned,  — 
its  chemical  condition  is  changed.  It  is 
evident  that  we  receive  something  which 
must  come  to  us  from  the  sun.  To  the 
sense  of  touch  it  appears  to  be  heat;  in 
the  eye  it  produces  the  sensation  of  light ; 
in  certain  substances  it  has  the  power  to 
produce  chemical  changes.  What  is  it  that 
we  receive  from  the  sun? 

Figure  247  represents  an  instrument 
called  a  radiometer.  The  moving  part  is 
a  small  vane  resting  on  the  point  of  a 
needle.  It  is  so  nicely  poised  on  this  pivot 
that  it  rotates  with  the  greatest  freedom.  Fig-  347- 
To  the  extremities  of  each  of  the  four  arms  of  the  vane 
are  attached  disks  of  aluminum,  which  are  white  on  one 
side  and  black  on  the  other.  The  whole  is  enclosed  in  a 
glass  bulb,  and  the  air  within  is  reduced  to  less  than  one- 
millionth  its  usual  density.  If  the  instrument  is  exposed 


282  RADIANT   ENERGY. 

to  the  sun  the  wheel  will  rotate  with  the  white  faces  in 
advance. 

In  just  what  manner  it  is  caused  to  rotate  does  not  con- 
cern us  at  present ;  but  the  fact  that  it  rotates,  and  that 
it  is  caused  to  rotate  directly  or  indirectly  by  something 
that  comes  from  the  sun,  is  pertinent  to  the  question  be- 
fore us.  Whenever  a  body  is  caused  to  move  or  increase 
its  rate  of  motion,  energy  must  be  imparted  to  it ;  hence 
energy  must  be  imparted  to  the  radiometer-vane  by  the  sun. 

That  which  we  receive  from  the  sun,  whether  it  affects 
the  sense  of  touch  or  of  sight,  or  produces  chemical  changes, 
is  in  reality  some  form  of  energy  and  is  one  and  the  same 
form  whatever  the  effect. 

261.  Ether  the  Medium  of  Motion.  —  If  we  receive 
the  energy  of  motion,  what  moves?  Our  atmosphere  is 
but  a  thin  mantle  covering  the  earth,  while  the  great  space 
that  separates  us  from  the  sun  contains  no  air  or  other 
known  substance.  But  empty  space  cannot  communicate 
motion.  It  is  assumed  —  it  is  necessary  to  assume  —  that 
there  is  some  medium  filling  the  interplanetary  space ; 
in  fact,  filling  all  space  otherwise  unoccupied,  a  medium 
by  which  motion  can  be  communicated  from  one  point  to 
another.  This  medium  has  received  the  name  of  ether. 

We  cannot  see,  hear,  feel,  taste,  smell,  weigh,  nor  meas- 
ure it.  What  evidence,  then,  have  we  that  it  exists? 
This:  phenomena  occur  just  as  they  would  occur  if  all 
space  were  filled  with  an  ethereal  medium  capable  of 
transmitting  motion;  we  have  been  able  to  account  for 
these  phenomena  on  no  other  hypothesis,  hence  our  belief 
in  the  existence  of  the  medium. 

The  transmission  of  energy  through  the  medium  of 
ether  is  called  radiation ;  energy  so  transmitted  is  called 


UNDULATORY  THEORY.  283 

radiant  energy,  and  the  body  emitting  energy  in  this 
manner  is  called  a  radiator. 

262.  TJndulatory   Theory ;    the  Sensation   of  Light. 

—  All  evidence  points  to  one  conclusion :  that  we  receive 
energy  from  the  sun  in  the  form  of  vibrations  or  waves ; 
that  a  portion  of  these  waves  having  suitable  wave-length 
are  capable  of  causing  through  the  eye  the  sensation  of 
light.  Such  as  affect  the  sense  of  sight  are  called  light- 
waves. This  is  known  as  the  undulatory  theory.  Accord- 
ing to  this  theory  light l  is  a  sensation  caused,  usually,  by 
the  action  of  ether-waves  on  the  organ  of  sight.  The  term 
light  is  commonly  applied  to  the  agent  which  produces  the 
sensation,  but  it  is  thought  that  in  a  scientific  treatise 
much  may  be  gained  in  many  ways  by  restricting  the  term 
to  the  sensation,  and  applying  to  the  agent  the  appropriate 
term  light-waves. 

All  ether-waves  are  capable  of  generating  heat  and, 
consequently,  of  causing  the  sensation  of  warmth.  A 
large  portion  of  the  ether-waves  are  also  capable  of  pro- 
moting chemical  action  in  certain  substances. 

263.  Sources    of    Light- waves,    Incandescence    and 
Phosphorescence.  —  Every   form   of  matter   when   suffi- 
ciently heated  emits   light-waves;   in  other  words,  when 
the  vibration  period  of  its  molecules  becomes  such  as  to 
create  ethereal  waves  that  are   capable  of  affecting  the 
sense  of  sight,  the  body  is  said  to  be  luminous.    This  con- 
dition is  termed  incandescence.     The  sun  and  fixed  stars 
are  in  a  condition  of  intense  incandescence.     Nearly  all 
the  artificial  sources  of  light-waves,  such  as  lamp  and  gas 
flames  and  electric  lamps,  depend  upon  the  development 
of  light-waves  mainly  through  the  incandescence  of  carbon. 

1  "  The  optical  sensations  are  Light,  Color,  and  Lustre."  —  Bain's  Mental  Science. 


284 


RADIANT   ENERGY. 


There  is  a  class  of  substances,  such  as  the  sulphides  of 
calcium,  strontium,  etc.,  which,  after  several  hours'  expos- 
ure to  light-waves,  absorb  their 
energy  (i.e.  their  molecules  ac- 
quire sympathetic  vibrations) 
without  becoming  hot,  and  in 
turn  emit  light-waves,  which  are 
quite  perceptible  in  a  dark  room 
for  several  hours  after  the  ex- 
posure. This  property  of  shining 
in  the  dark  after  having  been 
exposed  to  light-waves  is  termed 
phosphorescence.  A  so-called  lumi- 
nous paint  is  prepared  and  ap- 
Fig.  848.  plied  to  certain  parts  of  bodies 

that  are  exposed  to  sunshine  during  the  day;  at  night 
those  parts  to  which  the  paint  is  applied  are  alone  lumi- 
nous. This  paint  may  be  used  for  a  variety  of  purposes, 
such  as  rendering  danger  signals,  door  numbers,  and  plates 
luminous  (Fig.  248),  etc. 

264.  Light- waves   travel   in   Straight  Lines.  —  The 

path  of  light-waves  admitted  into  a  darkened  room  through 
a  small  aperture,  as  indicated  by  the  illuminated  dust,  is 
perfectly  straight.  An  object  is  seen  by  means  of  light- 
waves which  it  sends  to  the  eye.  A  small  object  placed  in 
a  straight  line  between  the  eye  and  a  luminous  point 
may  intercept  the  light-waves  in  that  path,  and  the  point 
become  invisible.  Hence  we  cannot  see  around  a  corner, 
or  through  a  bent  tube. 

265.  Ray,  Beam,  Pencil.  —  Any  line  RR,  Figure  249, 
which  pierces  the    surface  of  an   ether-wave  ab  perpen- 


RAY,   BEAM,   PENCIL.  285 

dicularly   is   called  a  ray.      The   term  "ray"  is   but  an 

expression  for  the  direction  in  which  motion  is  propagated, 

and  along  which  the  successive  effects  of  ether-ivaves  occur. 

If  the  wave-surface  a'b'  is  a  plane, 

the  rays  R'R'  are  parallel,  and  a 

collection  of  such  rays  is  called  a 

beam.     If  the  wave-surface  a"b'f 

is  spherical  or  concave,  the  rays 

R"R"  have  a  common  point  at 

the  center  of   curvature ;   and   a 

collection  of  such  rays  is  called 

a  pencil. 

266.  Transparent,    Translu- 
cent,    and     Opaque     Bodies. — 

Bodies  are  transparent,  translu- 
cent, or  opaque,  according  to 
the  manner  in  which  they  act 
upon  the  light-waves  which  pass 

Fig.  249. 

through  them.  Generally  speak- 
ing, those  objects  are  transparent  that  allow  other  objects 
to  be  seen  through  them  distinctly,  e.g.  air,  glass,  and 
water.  Those  objects  are  translucent  that  allow  light- 
waves to  pass,  but  in  such  a  scattered  condition  that 
objects  are  not  seen  distinctly  through  them,  e.g.  fog, 
ground  glass,  and  oiled  paper.  Those  objects  are  opaque 
that  apparently  cut  off  all  the  light-waves  and  prevent 
objects  from  being  seen  through  them. 

267.  Luminous    and    Illuminated   Objects.  —  Some 
bodies  are  seen  by  means  of  light-waves  which  they  emit, 
e.g.  the  sun,  a  candle  flame,  and  a  "live  "coal;  they  are 
called  luminous   bodies.     Other  bodies   are  seen  only  by 


286  EADIANT  ENEEGY. 

means  of  light-waves  which  they  receive  from  luminous 
ones;  and  when  thus  rendered  visible  are  said  to  be 

illuminated,  e.g.  the  moon,  a 
man,  a  cloud,  and  a  "dead" 
coal. 

Every  point  of  a  luminous 
body  is  an  independent  source  of 
light-waves,  and  emits  light-waves 
in  every  direction.  Such  a  point 
is  called  a  luminous  point.  In 
Figure  250  there  are  represented 
a  few  of  the  infinite  number  of 
rig.  »5o.  pencils  emitted  by  three  lumi- 

nous points  of  a  candle  flame.  Every  point  of  an  illumi- 
nated object,  ab,  receives  light-waves  from  every  luminous 
point. 

268.    Images  formed  through  Small  Apertures. 

Experiment  227.  —  Cut  a  hole  about  4  inches  square  in  one  side  of 
a  box ;  cover  the  hole  with  tin-foil,  and  prick  a  hole  in  the  foil  with  a 
pin.  Place  the  box  in  a  darkened  room,  and  a  candle  flame  in  the  box 
near  to  the  pin-hole.  Hold  an  oiled-paper  screen  before  the  hole  in 
the  foil ;  an  inverted  image  of  the  candle  flame  will  appear  upon  the 
translucent  paper. 

An  image  is  a  kind  of  picture  of  an  object.  If  light- 
waves from  objects  illuminated  by  the  sun,  e.g.  trees, 
houses,  clouds,  or  even  an  entire  landscape,  are  allowed 
to  pass  through  a  small  aperture  in  a  window  shutter 
and  strike  a  white  wall  in  a  dark  room,  inverted  im- 
ages of  the  objects  in  their  true  colors  will  appear  upon 
it.  The  cause  of  these  phenomena  is  easily  understood. 
When  no  screen  intervenes  between  the  candle  and  the 
screen  A,  Figure  251,  every  point  of  the  screen  receives 


SHADOWS.  287 

light-waves  from  every  point  of  the  candle ;  consequently, 
on  every  point  on  A,  im- 
ages of  the  infinite  num- 
ber of  points  of  the  candle 
are  formed.  The  result 
of  the  confusion  of  images 
is  equivalent  to  no  image. 
But  let  the  screen  B, 
containing  a  small  hole, 
be  interposed ;  then,  since  Fig.  251. 

light- waves  travel  only  in  straight  lines,  the  point  Y' 
can  only  receive  an  image  of  the  point  Y,  the  point  Z' 
only  of  the  point  Z,  and  so  for  intermediate  points ; 
hence  a  distinct  image  of  the  object  must  be  formed  on 
the  screen  A. 

That  an  image  may  be  distinct,  the  rays  from  different 
points  of  the  object  must  not  mix  on  the  image,  but  all  rays 
from  each  point  on  the  object  must  be  carried  to  its  own 
point  on  the  image. 

269.    Shadows. 

Experiment  228.  —  Procure  two  pieces  of  tin  or  cardboard,  one 
18cra  square,  the  other  3cm  square.  Place  the  first  between  a  white 
wall  and  a  candle  flame  in  a  darkened  room.  The  opaque  tin  inter- 
cepts the  light-waves  that  strike  it,  and  thereby  excludes  light-waves 
from  a  space  behind  it. 

This  space  is  called  a  shadow.  That  portion  of  the  sur- 
face of  the  wall  that  is  darkened  is  a  section  of  the  shadow, 
and  represents  the  form  of  a  section  of  the  body  that 
intercepts  the  light-waves.  A  section  of  a  shadow  is  fre- 
quently for  convenience  called  a  shadow.  Notice  that  the 
shadow  is  made  up  of  two  distinct  parts,  —  a  dark  center 
bordered  on  all  sides  by  a  much  lighter  fringe.  The 


288  RADIANT   ENERGY. 

dark  center  is  called  the  umbra,  and  the  lighter  envelope 
is  called  the  penumbra. 

Experiment  229.  — Carry  the  tin  nearer  the  wall,  and  notice  that 
the  penumbra  gradually  disappears  and  the  outline  of  the  umbra  be- 
comes more  distinct.  Employ  two  candle  names,  a  little  distance  apart, 
and  notice  that  two  shadows  are  produced.  Move  the  tin  toward  the 
wall,  and  the  two  shadows  approach  one  another,  then  touch,  and 
finally  overlap.  Notice  that  where  they  overlap  the  shadow  is  deepest. 
This  part  gets  no  light-waves  from  either  flame,  and  is  a  section  of 
the  umbra ;  while  the  remaining  portion  gets  light-waves  from  one 
or  the  other,  and  is  a  section  of  the  penumbra.  Or  move  the  eye 
across  the  shadow  from  side  to  side  and  see  parts  of  the  flame  in  the 
penumbra,  but  none  in  the  umbra. 

Just  so  the  umbra  of  every  shadow  is  the  part  that  gets  no 
light-waves  from  a  luminous  body,  while  the  penumbra  is 
the  part  that  gets  light-waves  from  some  portion  of  the  body, 
but  not  from  the  whole. 

Experiment  230.  —  Repeat  the  above  experiments,  employing  the 
smaller  piece  of  tin,  and  note  all  differences  in  phenomena  that  occur. 
Hold  a  hair  in  the  path  of  the  sun's  waves,  about  a  quarter  of  an  inch 
in  front  of  a  fly-leaf  of  this  book,  and  observe  the  shadow  cast  by 
the  hair.  Then  gradually  increase  the  distance  between  the  hair 
and  the  leaf,  and  note  the  change  of  phenomena. 

If  the  source  of  light-waves  were  a  single  luminous  point,  as  A  (Fig. 
^^    252),  the  shadow  of  an  opaque  body  B 
—  l-~^  s    would  be  of  infinite  length,  and  would 


consist  only  of  an  umbra.     But  if  the 
source  of  light-waves  has  a  sensible  size, 
853.  the  opaque  body  will  intercept  just  as 

many  separate  pencils  as  there  are  luminous  points,  and  consequently  will 
cast  an  equal  number  of  independent  shadows. 

Let  AB  (Fig.  253)  represent  a  luminous  body,  and  CD  an  opaque  body. 
The  pencil  from  the  luminous  point  A  will  be  intercepted  between  the 
lines  CF  and  DG,  and  the  pencil  from  B  will  be  intercepted  between  the 


PHOTOMETRY,   VISUAL  ANGLE,   ETC.  289 

wave-lines  CE  and  DF.    Hence  the  light-waves  will  be  wholly  excluded  only 
from  the  space  between  the  lines  CF  and  DF,  which  enclose  the  umbra. 


Fig.  353. 

The  enveloping  penumbra,  a  section  of  which  is  included  between  the  lines 
CE  and  CF,  and  between  DF  and  DG,  receives  light-waves  from  certain 
points  of  the  luminous  body,  but  not  from  all. 


Section  II. 

PHOTOMETRY,   VISUAL   ANGLE,   ETC. 

27O.    Law  of  Inverse  Squares. 

Experiment  231.  —Arrange  apparatus  as  follows :  Draw  a  straight 
chalk^line  across  a  table,  and  place  at  right  angles  to  this  line  a  row 
of  four  lighted  candles,  and  on  the  same  line,  at  a  distance,  a  single 
lighted  candle.  Half-way  between  this  candle  and  the  row  of  candles 
place  a  paper  disk  having  a  circular  translucent  spot  in  the  center,  as  in 
Figure  254.  It  is  evident  that  one  side  of  the  paper  receives  four  times 
the  radiant  energy  that  the  other  does.  Move  the  row  of  candles 


290  KADIANT   ENERGY. 

slowly  away  from  the  paper,  or  move  the  single  candle  toward  the 
paper,  until  a  point  is  found  where  the  spot  nearly  disappears.  The 
paper  now  receives  the  same  amount  of  energy  from  the  single  flame 

as  from  the  four  flames,  but 
it  will  be  found  that  the 
row  of  flames  is  twice  as 
far  from  the  paper  as  the 
single  flame. 

Thus,  by   doubling 
Fig.  254.  the   distance,   the   in- 

tensity of  illumination  is  diminished  fourfold.  In  a  similar 
manner  it  may  be  shown  that  at  three  times  the  distance 
it  takes  nine  flames  to  be  equivalent  to  one  flame.  Hence, 
the  intensity  of  illumination  diminishes  as  the  square  of  the 
distance  increases.  This  is  called  the  law  of  inverse  squares. 

Experiment  232.  —  Introduce  the  paper  disk,  as  above,  between 
a  candle  flame  and  a  kerosene  or  a  gas  flame,  and  so  regulate  the  dis- 
tance that  the  central  spot  will  disappear ;  then  calculate  the  relative 
intensities  of  the  flames  in  accordance  with  the  law  of  inverse  squares. 

This  is  the  method  usually  employed  by  gas  inspectors 
for  testing  the  intensity  of  light-waves.  Apparatus  ar- 
ranged for  this  purpose  is  called  a  photometer.  "The 
candle  power,  which  is  the  unit  of  intensity  generally  em- 
ployed in  photometry,  is  the  intensity  of  the  flame  of  a 
sperm  candle  weighing  one-sixth  of  a  pound,  and  burning 
one  hundred  and  twenty  grains  an  hour." 

The  relative  brightness  of  the  common  sources  of  light- 
waves are  approximately  as  follows : l  — 

Sun  at  its  surface 190,000  candle  power. 

Most  powerful  electric  arc 55,900      " 

Incandescent  calcium 1,300      "          " 

Ordinary  gas-burner 12  to  16      "          " 

Standard  candle 1      " 

i  C.  A.  Young. 


PHOTOMETRY,   VISUAL   ANGLE,   ETC.  291 

271.    Visual  Angle. 

Experiment  233.  —  Prick  a  pin-hole  in  a  card,  place  an  eye  near 
the  hole,  and  look  at  a  pin  about  20cm  distant.  Then  bring  the  pin 
slowly  toward  the  eye,  and  the  dimensions  of  the  pin  will  appear  to 
increase  as  the  distance  diminishes. 

Why  is  this  ?  We  see  an  object  by  means  of  its  image 
formed  on  the  retina  of  the  eye ;  and  its  apparent  magni- 
tude is  determined  by  the  extent  of  the  retina  covered  by 
its  image.  Rays  proceeding  from  opposite  extremities  of 
an  object,  as  AB  (Fig.  255),  meet  and  cross  one  another 


Fig.  255. 

in  the  window  of  the  eye,  called  the  pupil.  Now,  as  the 
distance  between  the  points  of  the  blades  of  a  pair  of 
scissors  depends  upon  the  angle  that  the  handles  form 
with  one  another,  so  the  size  of  the  image  formed  on  the 
retina  depends  upon  the  size  of  the  angle,  called  the  visual 
angle,  formed  by  these  rays  as  they  enter  the  eye.  But 
the  size  of  the  visual  angle  diminishes  as  the  distance  of 
the  object  from  the  eye  increases,  as  shown  in  the  dia- 
gram ;  e.g.  at  twice  the  distance  the  angle  is  one-half  as 
great ;  at  three  times  the  distance  the  angle  is  one-third 
as  great ;  and  so  on.  Hence,  distance  affects  the  apparent 
size  of  an  object.  Our  judgment  of  size  is,  however,  influ- 
enced by  other  things  besides  the  visual  angle  which  they 
subtend. 


292  RADIANT   ENERGY. 

272.  Velocity  of  Light- Waves.  —  By  several  ingenious 
methods  it  lias  been  ascertained  that  light- waves  travel  at 
the  rate  of  about  186,000  miles  in  a  second,  a  velocity 
which  would  enable  them  to  go  around  the  earth  about 
seven  times  in  a  second.  Sound-waves  travel  in  air  at  the 
rate  of  only  about  one-fifth  of  a  mile  per  second.  This 
great  difference  can  be  accounted  for  only  on  the  suppo- 
sition that  the  rarity  and  elasticity  of  ether  are  enormously 
greater  than  that  of  air. 


Section  III. 

REFLECTION    OF  LIGHT-WAVES. 

273.    Law  of  Reflection. 

Experiment  234.  —  Look  through  the  hole  in  the  metal  band  (Fig. 
256),  marked  zero,  at  the  mirror.  You  see  in  the  mirror  an  image  of 

the  hole  through  which  you 
are  looking,  but  you  do  not 
see  the  image  of  any  of 
the  other  holes.  Rays  that 
pass  through  this  hole  strike 
the  mirror  perpendicularly, 
Fig.  256.  an(j  are  cai}ed  incicient  rays. 

The  reflected  rays  are  thrown  back  in  the  same  line  and  through  the 
same  hole  that  the  incident  rays  travel  to  the  eye. 

Hold  a  candle  flame  at  one  of  the  other  holes  (or  stop  it  with  a  fin- 
ger), e.g.  at  the  hole  marked  10.  You  can  see  the  reflected  rays  of  the 
candle  flame  only  through  the  hole  of  the  same  number  on  the  other 
side,  i.e.  for  example,  incident  rays  making  an  angle  of  10°  (called  the 
angle  of  incidence}  with  the  perpendicular  to  the  surface  of  the  mirror 
is  reflected  at  an  angle  of  10°  (called  the  angle  of  reflection}  with  the 
perpendicular.  The  angle  of  reflection  is  always  equal  to  the  angle  of 
incidence. 


REFLECTION    OF   LIGHT- WAVES.  293 

274.  Reflection  from  Plane  Mirrors;  Virtual  Im- 
ages. —  MM  (Fig.  257)  represents 
a  plane  mirror,  and  AB  a  pencil  of 
divergent  rays  proceeding  from  the 
point  A  of  an  object  AH.  Erect- 
ing perpendiculars  at  the  points  of 
incidence,  or  the  points  where  these 
rays  strike  the  mirror,  and  mak- 
ing the  angles  of  reflection  equal 
to  the  angles  of  incidence,  the 
paths  BC  and  EC  of  the  reflected 
rays  are  found.  Fis-  257. 

It  appears  that  divergent  incident  rays  remain  divergent 
after  reflection  from  a  plane  mirror.  (In  like  manner  con- 
struct a  diagram,  and  show  that  parallel  incident  rays  are 
parallel  after  reflection.}  Construct  another  diagram,  and 
show  that  convergent  incident  rays  are  convergent  after  re- 
flection, i.e.  reflection  from  a  plane  surface  does  not  alter 
the  angle  between  rays.  To  an  eye  placed  at  C,  the  points 
from  which  the  rays  appear  to  come  are  of  course  in  the 
direction  of  the  rays  as  they  enter  the  eye.  These  points 
may  be  found  by  continuing  the  rays  CB  and  CE  behind 
the  mirror,  till  they  meet  at  the  points  D  and  N.  Every 
point  of  the  object  AH  sends  out  its  pencil  of  rays ;  and 
those  that  strike  the  mirror  at  a  suitable  angle  to  be 
reflected  to  the  eye,  produce  on  the  retina  of  the  eye  an 
image  of  that  point,  and  the  point  from  which  the  light- 
waves appear  to  emanate  is  found,  as  previously  described. 
Thus,  the  pencils  EC  and  BC  appear  to  emanate  from  the 
points  N  and  D ;  and  the  whole  body  of  light-waves  re- 
ceived by  the  eye  seems  to  come  from  an  apparent  object 
ND  behind  the  mirror.  This  apparent  object  is  called  an 
image;  but  as,  of  course,  there  can  be  no  real  image 


294  BADIANT   ENERGY. 

formed  there,  it  is  called  a  virtual  or  an  imaginary  image. 
It  will  be  seen,  by  construction,  that  an  image  in  a  plane 
mirror  appears  as  far  behind  the  mirror  as  the  object  is  in 
front  of  it,  and  is  of  the  same  size  and  shape  as  the  object. 

275.   Reflection  from  Concave  Mirrors.  —  Let   MM' 

(Fig.  258),  represent  a  section  of  a  concave  mirror,  which 
may  be  regarded  as  a  small  part  of  a  hollow  spherical 
shell  having  a  polished  interior  surface.  The  distance 
MM1  is  called  the  diameter  of  the  mirror.  C  is  the  center 

of  the  sphere,  and  is 
called  the  center  of 
curvature.  G  is  the 
vertex  of  the  mirror. 
A  straight  line  DG 
drawn  through  the 
center  of  curvature 
and  the  vertex  is 
rig.  258.  called  the  principal 

axis  of  the  mirror.  A  concave  mirror  may  be  considered 
as  made  up  of  an  infinite  number  of  small  plane  surfaces. 
All  radii  of  the  mirror,  as  CA,  CG,  and  CB,  are  perpen- 
dicular to  the  small  planes  which  they  strike.  If  C  be  a 
luminous  point,  it  is  evident  that  all  light-waves  emanating 
from  this  point,  and  striking  the  mirror,  will  be  reflected 
to  its  source  at  C. 

Let  E  be  any  luminous  point  in  front  of  a  concave 
mirror.  To  find  the  direction  that  rays  emanating  from 
this  point  take  after  reflection,  draw  any  two  lines  from 
this  point,  as  EA  and  EB,  representing  two  of  the  infi- 
nite number  of  rays  composing  the  divergent  pencil  that 
strikes  the  mirror.  Next,  draw  radii  to  the  points  of  inci- 
dence A  and  B,  and  draw  the  lines  AF  and  BF,  making 


REFLECTION   OF   LIGHT-WAVES.  295 

the  angles  of  reflection  equal  to  the  angles  of  incidence. 
Place  arrow-heads  on  the  lines  representing  rays  to  indi- 
cate the  direction  of  the  motion.  The  lines  AF  and  BF 
represent  the  direction  of  the  rays  after  reflection. 

It  will  be  seen  that  the  rays  after  reflection  are  con- 
vergent, and  meet  at  the  point  F,  called  the  focus.  This 
point  is  the  focus  of  all  reflected  rays  that  emanate  from 
the  point  E.  It  is  obvious  that  if  F  were  the  luminous 
point,  the  lines  AE  and  BE  would  represent  the  reflected 
rays,  and  E  would  be  the  focus  of  these  rays.  Since  the 
relation  between  the  two  points  is  such  that  light-waves 
emanating  from  either  one  are  brought  by  reflection  to  a 
focus  at  the  other,  these  points  are  called  conjugate  foci.  Con- 
jugate foci  are  two  points  so  related  that  the  image  of  either  is 
formed  at  the  other.  The  rays  EA  and  EB  emanating  from 
E  are  less  divergent  than  rays  FA  and  FB,  emanating  from 
a  point  F  less  distant  from  the  mirror,  and  striking  the 
same  points.  Rays  emanating  from  D,  and  striking  the 
same  points  A  and  B,  will  be  still  less  divergent ;  and  if 
the  point  D  were  removed  to  a  distance  of  many  miles, 
the  rays  incident  at  these  points  would  be  very  nearly 
parallel.  Hence  rays  may  be  regarded 
as  practically  parallel  when  their  source 
is  at  a  very  great  distance,  e.g.  the  sun's 
rays.  If  a  sunbeam,  consisting  of  a 
bundle  of  parallel  rays,  as  EA,  DG, 
and  HB  (Fig.  259),  strike  a  concave  Fig.  259. 

mirror  parallel  with  its  principal  axis,  these  rays  become 
convergent  by  reflection,  and  meet  at  a  point  (F)  in  the 
principal  axis.  This  point,  called  the  principal  focus,  is 
just  half-way  between  the  center  of  curvature  and  the 
vertex  of  the  mirror. 

On  the  other  hand,  it  is  obvious  that  divergent  rays 


296  RADIANT    ENERGY. 

emanating  from  the  principal  focus   of  a   concave   mirror 
become  parallel  by  reflection. 

If  a  small  piece  of  paper  is  placed  at  the  principal  focus 
of  a  concave  mirror,  and  the  mirror  is  exposed  to  the  par- 
allel rays  of  the  sun,  the  paper  will  quickly  burn. 

Construct  a  diagram,  and  show  that  rays  proceeding 
from  a  point  between  the  principal  focus  and  the  mirror 
are  divergent  after  reflection,  but  less  divergent  than  the 
incident  rays.  Reversing  the  direction  of  the  rays  the 
same  diagram  will  show  that  convergent  rays  are  rendered 
more  convergent  by  reflection  from  concave  mirrors. 

The  general  effect  of  a  concave  mirror  is  to  increase  the 

convergence  or  to 
decrease  the  diver- 
gence of  incident 
rays. 

The  statement,  that 
parallel  rays  after  re- 
flection from  a  concave 
mirror  meet  at  the  prin- 
cipal focus,  is  only  ap- 
proximately true.  The 
smaller  the  diameter  of 
the*  mirror,  the  more  nearly  true  is  the  statement.  It  is  strictly  true  only 
of  parabolic  mirrors.  Such  are  used  in  the  head-lights  of  locomotives. 

276.   Formation  of  Images. 

Experiment  235.  —  Hold  some  object,  e.g.  a  rose,  as  ab  (Fig.  260), 
a  few  feet  in  front  of  a  concave  mirror.  Looking  in  the  direction  of 
the  axis  of  the  mirror  you  see  a  small  inverted  image  AB  of  the  object 
between  the  center  of  curvature,  C,  of  the  mirror  and  its  principal 
focus  F. 

Evidently  if  AB  represent  an  object  placed  between  the  principal 
focus  and  center  of  curvature,  then  ab  will  represent  the  image  of  the 
object.  The  image  in  this  case  may  be  projected  upon  a  screen,  but 
it  will  not  be  so  bright  as  in  the  former  case,  because  the  light-waves 
are  spread  over  a  larger  surface. 


REFLECTION   OF  LIGHT-WAVES.  297 

Experiment  236.  —  Place  a  candle  in  an  otherwise  dark  room  20 
feet  from  the  mirror,  catch  the  focused  light-waves  upon  a  paper 
screen,  and  show  that  the  focus  is  half-way  between  the  vertex  and 
the  center  of  curvature  of  the  mirror. 

Experiment  237.  —  Advance  the  distant  candle  flame  toward  the 
mirror,  moving  it  up  and  down.  (1)  Show  that  the  focus  advances  to 
meet  the  flame,  and  that  when  the  flame  is  raised,  the  focus  is  depressed, 
and  the  converse.  (2)  Show  that  when  the  flame  is  at  the  center  of 
curvature,  there  also  is  the  focus.  (3)  Show  that  when  the  flame  is  be- 
tween the  center  of  curvature  and  the  principal  focus,  the  focus  of  the 
flame  is  farther  away  than  the  center  of  curvature.  (4)  Show  that 
when  the  flame  is  at  the  principal  focus,  the  reflected  rays  are  parallel, 
or  the  focus  is  at  an  infinite  distance.  (5)  Show  that  when  the  flame  is 
still  nearer,  the  reflected  rays  diverge  and  appear  to  come  from  a  point 
behind  the  mirror.  (6)  Notice  that  in  all  cases  except  the  last  the  im- 
ages are  real  and  inverted,  and  that  in  all  cases  where  a  real  image  is 
formed,  the  flame  and  the  image  may  change  places. 

Experiment  238.  —  Form  a  real  image  of  the  flame  between  your- 
self and  the  mirror ;  view  the 
image  through  a  convex  lens 
(Fig.  280) ;  show  that  the  im- 
age can  be  magnified  by  a 
convex  lens,  and  thereby  illus- 
trate the  principle  of  an  astro- 
nomical reflecting  telescope. 

Construct  the  image  of 
an  object  placed  between  Fis-  SGI. 

the  principal  focus  and  the  mirror,  as  in  Figure  261.  It 
will  be  seen  in  this  case  that  a  pencil  of  rays  proceeding 
from  any  point  of  an  object,  e.g.  D,  has  no  actual  focus, 
but  appears  to  proceed  from  a  virtual  focus  D',  back  of  the 
mirror ;  and  so  with  other  points,  as  E.  The  image  of  an 
object  placed  between  the  principal  focus  and  the  mirror  is 
virtual,  erect,  larger  than  the  object,  and  is  back  of  the  mirror. 

277.  Convex  Mirrors.  —  The  general  effect  of  convex 
mirrors  is  to  separate  incident  rays.  In  them  all  images 
are  virtual,  erect,  and  smaller  than  the  objects. 


298  KADIANT   ENERGY. 

Section  IV. 

REFRACTION. 

278.    Introductory  Experiments. 

Experiment  239.  —  Into  a  darkened  room  admit  a  sunbeam  so 
that  its  rays  may  fall  obliquely  on  the  bottom  of  the  basin  (Fig.  262), 

and  note  the  place  on  the  bottom 
where  the  edge  of  the  shadow  DE 
cast  by  the  side  of  the  basin  DC 
meets  the  bottom  at  E.  Then, 
without  moving  the  basin,  fill  it 
even  full  with  water  slightly  clouded 
with  milk  or  with  a  few  drops  of  a 
solution  of  mastic  in  alcohol.  It 
will  be  found  that  the  edge  of  the 
shadow  has  moved  from  DE  to  DF, 
and  meets  the  bottom  at  F.  Beat 
Fig.  268.  a  Blackboard  rubber,  and  create  a 

cloud  of  dust  in  the  path  of  the  beam  in  the  air,  and  you  will  dis- 
cover that  the  rays  GD  that  graze  the  edge  of  the  basin  at  D  be- 
come bent  at  the  point  where  they  enter  the  water,  and  now  move 
in  the  bent  line  GDF,  instead  of,  as  formerly,  in  the  straight  line  GF. 
The  path  of  the  line  in  the  water  is  now  nearer  to  the  vertical  side  DC  ; 
in  other  words,  this  part  of  the  beam  is  more  nearly  vertical  than  before. 
Experiment  240.  — Place  a  coin  (A,  Fig.  263)  on  the  bottom  of 
an  empty  basin,  so  that,  as  you  look  through  a  small  hole  in  a  card 
BC  over  the  edge  of  the  vessel,  the  coin  is 
just  out  of  sight.  Then,  without  moving  the 
card  or  basin,  fill  the  latter  with  water.  Now, 
on  looking  through  the  aperture  in  the  card, 
the  coin  is  visible.  The  beam  AE,  which 
formerly  moved  in  the  straight  line  AD,  is 
now  bent  at  E,  where  it  leaves  the  water, 
and,  passing  through  the  aperture  in  the  card, 
enters  the  eye.  Observe  that,  as  the  beam  FiS*  263> 

from  the  water  into  the  air,  it  is  turned  farther  from  a  verti- 


REFRACTION.  299 

cal  line  EF ;  in  other  words,  the  beam  is  farther  from  the  vertical  than 
before. 

Experiment  241.  —  From  the  same  position  as  in  the  last  experi- 
ment, direct  the  eye  to  the  point  G  in  the  basin  filled  with  water. 
Reach  your  hand  around  the  basin,  and  place  your  finger  where  that 
point  appears  to  be.  On  examination,  it  will  be  found  that  your 
finger  is  considerably  above  the  bottom.  Hence,  the  effect  of  the  bend- 
ing of  rays,  as  they  pass  obliquely  out  of  water,  is  to  cause  the  bottom  to 
appear  more  elevated  than  it  really  is ;  in  other  words,  to  cause  the  water 
to  appear  shallower  than  it  is. 

Experiment  242. —  Thrust  a  pencil  obliquely  into  water  ;  it  will 
appear  shortened,  bent  at  the  surface  of  the  water,  and  the  immersed 
portion  elevated. 

Experiment  243.  —  Place  a  piece  of  wire  (Fig.  264)  vertically  in 
front  of  the  eye,  and  hold  a  narrow  strip  of  thick  plate  glass  horizon- 
tally across  the  wire,  so  that  the  light-waves  from  the  wire 
may  pass  obliquely  through  the  glass  to  the  eye.  The  wire 
will  appear  to  be  broken  at  the  two  edges  of  the  glass,  and 
the  intervening  section  will  appear  to  the  right  or  left  accord- 
ing to  the  inclination  of  the  glass ;  but  if  the  glass  is  not 
inclined  to  the  one  side  or  the  other,  the  wire  does  not 
appear  broken.  Fig* 

Experiment  244.  — Partly  fill  the  cell  (Fig.  147)  with  carbon 
bisulphide,  then  add  water.  Place  the  cell  in  the  path  of  a  beam  re- 
flected from  a  porte  lumiere.  Place  vertically  in  front  of  the  cell  a 
wire,  and  project  with  a  lens  a  shadow  of  the  wire  on  a  screen.  Turn 
the  cell  obliquely,  as  in  the  last  experiment,  and  notice  the  difference 
in  the  refracting  power  of  the  two  liquids. 

Experiment  245.  —  Partly  fill  the  same  cell  with  water.  Focus 
ifc  on  the  screen  so  that  the  surface  of  the  water  will  be  visible.  Add 
a  lump  of  ice  on  the  water.  Observe  the  streakiness  caused  by  differ- 
ence in  the  density  of  water  at  different  temperatures. 

Experiment  246.  —  Project  Avith  a  lens  a  luminous  circle  on  a 
screen.  Hold,  a  few  feet  in  front  of  the  screen,  a  candle  flame  in  the 
path  of  the  light-waves.  Observe  the  wavy  streakiness  arising  from 
the  changing  density  of  the  air  and  convection  currents. 

When  a  light-beam  passes  from  one  medium  into  another 
of  different  density,  it  is  bent  or  refracted  at  the  boundary 


300  RADIANT  ENERGY. 

plane  between  the  two  media,  unless  it  falls  exactly  per- 
pendicularly on  this  plane.  If  it  pass  into  a  denser 
medium,  it  is  refracted  toward  a  perpendicular  to  this  plane  ; 
if  into  a  rarer  medium,  it  is  refracted  from  the  perpendicu- 
lar. The  angle  GDO  (Fig.  262)  is  called  the  angle  of  in- 
cidence; FDN,  the  angle  of 
refraction  ;  and  EDF,  the  an- 
gle of  deviation. 

279.  Cause  of  Refraction. 

—  Careful  experiments  have  proved  that 
the  velocity  of  light-waves  is  less  in  a 
dense  than  in  a  rare  medium.  Let  the 
series  of  parallel  lines  AB  (Fig.  265) 
represent  a  series  of  wave-fronts  leav- 
ing an  object  C,  and  passing  through 
a  rectangular  piece  of  glass  DE,  and 
constituting  a  beam.  Every  point 
in  a  wave-front  moves  with  equal 

Fig.  265.  velocity  as   long  as  it  traverses  the 

same  medium ;  but  the  point  a  of  a  given  wave  ab  enters  the  glass  first, 
and  its  velocity  is  impeded,  while  the  point  b  retains  its  original  velocity ; 
so  that,  while  the  point  a  moves  to  a',  b  moves  to  b',  and  the  result  is 
that  the  wave-front  assumes  a  new  direction  (very  much  in  the  same 
manner  as  a  line  of  soldiers  execute  a  wheel),  and  a  ray  or  a  line  drawn 
perpendicularly  through  the  series  of  waves  is  turned  out  of  its  original 
direction  on  entering  the  glass.  Again,  the  extremity  c  of  a  given  wave- 
front  cd  first  emerges  from  the  glass,  when  its  velocity  is  immediately 
quickened;  so  that,  while  d  advances  to  d',  c  advances  to  c',  and  the 
direction  of  the  ray  is  again  changed.  The  direction  of  the  ray,  after 
emerging  from  the  glass,  is  parallel  to  its  direction  before  entering  it,  but 
it  has  suffered  a  lateral  displacement.  Let  C  represent  a  section  of  the 
wire  used  in  Experiment  262,  and  the  cause  of  the  phenomenon  observed 
will  be  apparent.  If  the  beam  strike  the  glass  perpendicularly,  all  points 
of  the  wave  will  be  checked  at  the  same  instant  on  entering  the  glass ; 
consequently  it  will  suffer  no  refraction. 

28O.  Index  of  Refraction.  —  The  deviation  of  light- 
waves, 'in  passing  from  one  medium  to  another,  varies 
with  the  medium  and  with  the  angle  of  incidence.  It 


REFRACTION. 


301 


diminishes  as  the  angle  of  incidence  diminishes,  and  is 
zero  when  the  incident  ray  is  normal  (i.e.  perpendicular 
to  the  surface  of  the  medi- 
um). It  is  highly  impor- 
tant, knowing  the  angle 
of  incidence,  to  be  able  to 
determine  the  direction 
which  a  ray  will  take  on 
entering  a  new  medium. 
Describe  a  circle  around 
the  point  of  incidence  A 
(Fig.  266)  as  a  center; 
through  the  same  point 
draw  IH  perpendicular  to  Fig-  366- 

the  surfaces  of  the  two  media,  and  to  this  line  drop  per- 
pendiculars BD  and  CE  from  the  points  where  the  circle 
cuts  the  ray  in  the  two  media.  Then  suppose  that  the 
perpendicular  BD  is  y8^  of  the  radius  AB  ;  now  this  frac- 
tion y8^  is  called  (in  trigonometry)  the  sine  of  the  angle 
DAB.  Hence,  T8-g-  is  the  sine  of  the  angle  of  incidence. 
Again,  if  we  suppose  that  the  perpendicular  CE  is  y6^  of 
the  radius,  then  the  fraction  y6^  is  the  sine  of  the  angle  of 
refraction.  The  sines  of  the  two  angles  are  to  one  another 
as  T%  :  y6^,  or  as  4  :  3.  The  quotient  (in  this  case  f  =  1.33+) 
obtained  by  dividing  the  sine  of  the  angle  of  incidence  by 
the  sine  of  the  angle  of  refraction  is  called  the  index  of 
refraction.  It  can  be  proved  to  be  the  ratio  of  the  velocity 
of  the  incident  to  that  of  the  refracted  light-waves.  It  is 
found  that  for  the  same  media  the  index  of  refraction  is 
a  constant  quantity  ;  i.e.  the  incident  ray  might  be  more 
or  less  oblique,  still  the  quotient  would  be  the  same. 

281 .  Indices  of  Refraction.  —  The  index  of  refraction  for  light- 
waves in  passing  from  air  into  water  is  approximately  f ,  and  from  air  into 


302 


RADIANT  ENERGY. 


glass  f ;  of  course,  if  the  order  is  reversed,  the  reciprocal  of  these  frac- 
tions must  be  taken  as  the  indices ;  e.g.  from  water  into  air,  the  index  is  f ; 
from  glass  into  air,  |.  When  a  ray  passes  from  a  vacuum  into  a  medium, 
the  refractive  index  is  greater  than  unity,  and  is  called  the  absolute  index 
of  refraction.  The  relative  index  of  refraction,  from  any  medium  A  into  another 
B,  is  found  by  dividing  the  absolute  index  of  B  by  the  absolute  index  of  A. 

The  refractive  index  varies  with  wave-length.    The  following  table  is 
intended  to  represent  mean  indices :  — 

TABLE  OF  ABSOLUTE  INDICES. 


Air  at  0°  C.,  and  760mm  pressure    .  1.000294 

Pure  water 1.33 

Alcohol 1.37 

Spirits  of  turpentine 1.48 

Humors  of  the  eye  (about)     .    .    .  1.35 


Carbon  bisulphide 1.641 

Crown  glass  (about) 1.53 

Flint  glass  (about) 1.61 

Diamond  (about) .2.5 

Lead  chromate 2.97 


282.    Critical    Angle;     Total    Reflection.  —  Let   SS' 

(Fig.  267)  represent  the  boundary  surface  between  two 
media,  and  AO  and  BO  incident  rays  in  the  more  refractive 
medium  (e.g.  glass)  ;  then  OD  and  OE  may  represent  the 
same  rays  respectively  after  they  enter  the  less  refractive 


Fig.  367. 

medium  (e.g.  air).  It  will  be  seen  that,  as  the  angle  of 
incidence  is  increased,  the  refracted  ray  rapidly  approaches 
the  surface  OS.  Now,  there  must  be  an  angle  of  incidence 
(e.g.  COM)  such  that  the  angle  of  refraction  will  be  90° ; 


REFRACTION.  303 

in  this  case  the  incident  ray  CO,  after  refraction,  will  just 
graze  the  surface  OS.  This  is  called  the  critical  or  limiting 
angle.  Any  incident  ray,  as  LO,  making  a  larger  angle 
with  the  normal  than  the  critical  angle,  cannot  emerge  from 
the  medium,  and  consequently  is  not  refracted.  Experi- 
ment shows  that  all  such  rays  undergo  internal  reflection ; 
e.g.  the  ray  LO  is  reflected  in  the  direction  ON.  Reflec- 
tion in  this  case  is  perfect,  and  hence  is  called  total  reflec- 
tion. Total  reflection  occurs  when  rays  in  the  more  refractive 
medium  are  incident  at  an  angle  greater  than  the  critical  angle. 

Surfaces  of  transparent  media,  under  these  circumstances,  constitute  the 
best  mirrors  possible.  The  critical  angle  diminishes  as  the  refractive  index 
increases.  For  water  it  is  about  48£°;  for  flint  glass,  38°  41' ;  and  for  the 
diamond,  23°  41'.  Light-waves  cannot,  therefore,  pass  out  of  water  into 
air  with  a  greater  angle  of  incidence  than  48£°.  The  brilliancy  of  gems, 
particularly  the  diamond,  is  due  in  part  to  their  extraordinary  power  of 
internal  reflection,  arising  from  their  large  indices  of  refraction. 

283.  Illustrations  of  Refraction  and  Total  Reflection. 

Experiment  247.  —  Observe  the  image  of  a  candle  flame  reflected 
by  the  surface  of  water  in  a  glass  beaker,  as  in  Figure  268. 

Experiment  248.  —  Thrust  the  closed  end  of  a  glass  test-tube 
(Fig.  269)  into  water,  and  incline  the  tube.  Look  down  upon. the 
immersed  part  of  the  tube,  and  its  upper  surface  will  look  like  bur- 


Fig.  268.  Fig.  869. 

nished  silver,  or  as  if  the  tube  contained  mercury.  Fill  the  test-tube 
with  water,  and  immerse  as  before ;  the  total  reflection  which  before 
occurred  at  the  surface  of  the  air  in  the  submerged  tube  now  disap- 
pears. Explain. 


304  RADIANT  ENERGY. 

f 

Section  V. 

DOUBLE  REFRACTION. 

284.   Double  Refraction. 

Experiment  249.  —  Through  a  card  make  a  pin-hole,  and  hold 
the  card  so  that  you  may  see  the  sky  through 
the  hole.  Now  bring  a  crystal  of  Iceland  spar 
(Fig.  270)  between  the  eye  and  the  card,  and 
look  at  the  hole  through  two  parallel  surfaces 
of  the  crystal.  There  will  appear  to  be  two 
holes,  with  light-waves  passing  through  each. 
Cause  the  crystal  to  rotate  in  a  plane  parallel 
with  the  card,  and  one  of  the  holes  will  appear 
to  remain  nearly  at  rest,  while  the  other  rotates 
Fig.  270.  around  the  first.  A  ray  na  immediately  on 

entering  the  crystal  is  divided  into  two  parts,  one  of  which  obeys  the 
regular  law  of  refraction ;  the  other  does  not.  The  former  is  called 
the  ordinary  ray ;  the  latter,  the  extraordinary  ray.  The  rays  issue  from 
the  crystal  parallel  with  each  other. 

In  every  direction  in  which  one  looks  through  the  crystal, 
except  that  parallel  to  AB,  objects  seen  through  it  appear 
double.  (See  Figure  271.)  The  line  AB  is  called  the  optic 


Fig.  371. 


axis  of  the  crystal,  and  is  a  line  around  which  the  mole- 
cules of  the  crystal  appear  to  be  arranged  symmetrically. 
A  crystal  is  called  uniaxial  when  it  has  only  one  optic  axis, 


PRISMS   AND   LENSES.  305 

and  biaxial  when  it  has  two  such  axes.  By  far  the  larger 
number  of  crystals  of  other  substances  possess  the  prop- 
erty of  causing  objects  seen  through  them  to  appear 
double.  This  phenomenon  is  called  double  refraction. 


Section  VI. 

PRISMS   AND   LENSES. 

285.  Optical  Prisms.  —  An  optical  prism  is  a  trans- 
parent, wedge-shaped  body.  Figure  272  represents  a 
transverse  section  of  such  a  prism.  Let  AB  be  a  ray 
incident  upon  one  of  its  surfaces.  On  entering  the  prism 
it  is  refracted  toward  the  normal,  and  takes  the  direc- 
tion BC.  On  emerging  from  the  prism  it  is  again  re- 
fracted, but  now  from  the  normal  in  the  direction  CD. 
The  object  that  emits  the 
ray  will  appear  to  be  at  F. 
Observe  that  the  ray  AB, 
at  both  refractions,  is  bent 
toward  the  thicker  part,  or 
base,  of  the  prism. 

286.  Lenses. — Any  trans-  Fig- 

parent  medium  bounded  by  two  spherical  surfaces,  or  by 
one  plane  and  the  other  curved,  is  a  lens. 

Experiment  250.  —  Procure  a  couple  of  lenses  thicker  in  the  mid- 
dle than  at  the  edge :  strong  spectacle  glasses,  or  the  large  lenses  in 
an  opera  glass,  will  answer.  Hold  one  of  the  lenses  in  the  sun's  rays, 
and  notice  the  path  of  the  beam  in  dusty  air  (made  so  by  striking 
together  two  blackboard  rubbers) ,  after  it  passes  through  the  lens ; 


306  RADIANT  ENERGY. 

also,  that  on  a  paper  screen  all  the  rays  may  be  brought  to  a  small 
circle,  or  even  to  a  point,  not  far  from  the  lens.  This  point  is  called 
the  focus,  and  its  distance  from  the  lens,  the  focal  length  of  the 
lens. 

Find  the  focal  length  of  this  lens,  then  of  the  second,  and  then  of 
the  two  together.  You  find  the  focal  length  of  the  two  combined  is 
less  than  of  either  alone,  and  learn  that  the  more  powerful  a  lens  or 
combination  of  them  is,  the  shorter  the  focal  length ;  that  is,  the  more 
quickly  are  the  parallel  rays  that  enter  different  parts  of  the  lens 
brought  to  cross  one  another. 

Experiment  251.  —  Procure  a  lens  thinner  in  the  middle  than  at 
its  edge.  One  of  the  small  lenses  or  eye-glasses  of  an  opera  glass  will 
answer.  Repeat  the  above  experiment  with  this  lens,  and  notice  that 
the  rays  emerging  from  the  lens,  instead  of  coming  to  a  point,  become 
spread  out. 

Lenses  are  of  two  classes,  converging  and  diverging, 
according  as  they  collect  rays  or  cause  them  to  diverge. 
Each  class  comprises  three  kinds  (Fig.  273)  :  — 

CLASS  I.  CLASS  II. 


1.  Double-convex     ]  Converging,  or  convex 


Converging, 
lenses  thi 


Plano-convex         !      lenses  thicker  in 
3.  Concavo-convex.   [     the  middle  than  at 
(or  meniscus)    J      the  edges. 


4.  Double-concave 


Convexo-concave 


- 


cave    lenses    thin- 


T>|  A_  J  Ci»VC       JtrUBCB         tJJlll- 

53S±2"S"i,  1     ner  in  the  middle 


than  at  the  edges. 


A  straight  line,  as  AB,  normal  to  both  surfaces  of  a 
lens,  and  passing  through  its  center  of  curvature,  is  called 

its  principal  axis. 
In  every  thin  lens 
there  is  a  point  in 
the  principal  axis 
called  the  optical 
rig.  273.  center.  Every  ray 

that  passes  through  it  has  parallel  directions  at  incidence 
and  emergence,  i.e.  can  suffer  at  most  only  a  slight  lateral 
displacement.  In  lenses  1  and  4  it  is  half-way  between 
their  respective  curved  surfaces.  A  ray,  drawn  through 


PRISMS   AND   LENSES.  307 

the  optical  center  from  any  point  of  an  object,  as  Aa 
(Fig.  282),  is  called  the  secondary  axis  of  this  point. 

287.  Effect  of  Lenses.  —  We  may,  for  convenience  of 
illustration,  regard  a  convex  lens  as  composed,  approxi- 
mately, of  two  prisms  placed  base  to  base,  as  A  (Fig. 
274),  and  a  concave  lens  as  composed  of  two  prisms  with 
their  edges  in  contact,  as  B.  Inasmuch  as  a  beam  ordi- 
narily strikes  a  lens  in  such  a  manner 
that  it  is  bent  toward  the  thicker  parts 
or  bases  of  these  approximate  prisms, 
it  is  obvious  that  the  lens  A  tends  to 
bend  the  transmitted  rays  toward  one 
another,  while  the  lens  B  tends  to 
separate  them.  The  general  effect  of  all  rig.  374. 

convex  lenses  is  to  converge  transmitted  rays ;  that  of  con- 
cave lenses,  to  cause  them  to  diverge.  Incident  rays  parallel 
with  the  principal  axis  of  a  convex  lens  are  brought  to 

a  focus  F  (Fig.  275) 
at  a  point  in  the  prin- 
cipal axis.  This  point 
is  called  the  principal 
focus,  i.e.  it  is  the  focus 
of  incident  rays  par- 
allel with  the  principal 
Fig'  375*  axis.  It  may  be  found 

by  holding  the  lens  so  that  the  rays  of  the  sun  may  fall 
perpendicularly  upon  it,  and  then  moving  a  sheet  of  paper 
back  and  forth  behind  it  until  the  image  of  the  sun 
formed  on  the  paper  is  brightest  and  smallest.  Or,  in  a 
room,  it  may  be  found  approximately,  by  holding  a  lens  at 
a  considerable  distance  from  a  window,  regulating  the 
distance  so  that  a  distinct  image  of  the  window  will  be 


308 


RADIANT   ENERGY. 


projected  upon  the  opposite  wall,  as  in  Figure  276.     The 
focal  length  is  the  distance  of  the  optical  center  of  the  lens 


Fig.  276. 

to  the  center  of  the  image  on  the  paper.  The  shorter 
this  distance  the  greater  is  the  power  of  the  lens. 

If  the  paper  is  kept  at  the  principal  focus  for  a  short  time, 
it  will  take  fire.  The  reason  is  apparent  why  convex  lens- 
es are  sometimes 
called  "  burning 
glasses."  A  pencil 
of  rays  emitted 
from  the  princi- 
pal focus  F  (Fig. 
275),  as  a  lumi- 
nous point,  be- 
Fig.  877.  comes  parallel  on 

emerging  from  a  convex  lens.  If  the  rays  emanate  from 
a  point  nearer  the  lens,  they  diverge  after  egress,  but  the 
divergence  is  less  than  before;  if  from  a  point  beyond 
the  principal  focus,  the  rays  are  rendered  convergent.  A 


PRISMS   AND   LENSES. 


309 


concave 


uunuctvc  lens  causes  parallel  incident  rays  to  diverge  as 
if  they  came  from  a  point,  as  F  (Fig.  277).  This  point  is 
therefore  its  principal  focus.  It  is,  of  course,  a  virtual 
focus. 

288.  Conjugate  Foci.  —  When  a  luminous  point  S  (Fig. 
278)  sends 
rays  to  a  con- 
vex lens,  the 
emergent  rays 
converge  to 
another  point 

S';  rays  sent  Fig. 

from  S'  to  the  lens  would   converge  to  S. 
thus  related  are  called  conjugate  f 


oc. 


Two  points 
The  fact  that  rays 
which  emanate  from  one  point  are  caused  by  convex 
lenses  to  collect  at  one  point,  gives  rise  to  real  images,  as 
in  the  case  of  concave  mirrors. 


Fig.  379. 

289.  Images  Formed. — Fairly  distinct  images  of  objects 
may  be  formed  through  very  small  apertures  (page  287)  ; 
but  owing  to  the  small  amount  of  radiant  energy  that  passes 
through  the  aperture,  the  images  are  very  deficient  in  bril- 
liancy. If  the  aperture  is  enlarged,  brilliancy  is  increased 


310  RADIANT   ENERGY. 

at  the  expense  of  distinctness.     A  convex  lens  enables  us  to 
obtain  both  brilliancy  and  distinctness  at  the  same  time. 

Experiment  252.  —  By  means  of  a  porte  lumiere  A  (Fig.  279)  in- 
troduce a  horizontal  beam  into  a  darkened  room.  In  its  path  place 
some  object,  as  B,  painted  in  transparent  colors  or 
photographed  on  glass.  (Transparent  pictures  are 
cheaply  prepared  by  photographers  for  sun-light  and 
lime-light  projections.)  Beyond  the  object  place  a 
convex  lens  L  (such  as  represented  in  Figure  279),  and 
beyond  the  lens  a  screen  S.  The  object  being  illu- 
minated by  the  beam,  all  the  rays  diverging  from 
any  point  a  are  bentf  by  the  lens  so  as  to  come  to- 
gether at  the  point  a'.  In  like  manner,  all  the  rays 
proceeding  from  c  are  brought  to  the  same  point  c' ; 
and  so  also  for  all  intermediate  points.  Thus,  out  of 
Fig.  380.  ^ne  innumerable  rays  emanating  from  each  of  the  in- 
numerable points  on  the  object,  those  that  reach  the  lens  are  guided 
by  it,  each  to  its  own  appropriate  point  in  the  image.  It  is  evident 
that  there  must  result  an  image,  both  bright  and  distinct,  provided  the 
screen  is  suitably  placed,  i.e.  at  the  place  where  the  rays  meet.  But  if 
the  screen  is  placed  at  S'  or  S",  it  is  evident  that  a  blurred  image 
will  be  formed.  Instead  of  moving  the  screen  back  and  forth,  in  order 
to  "  focus  "  the  rays  properly,  it  is  customary  to  move  the  lens. 

Experiment  253.  —  Make  a  series  of  experiments  similar  to  those 
(Experiment  237)  with  the  concave  mirror.  Ascertain  the  focal  length 
of  the  convex  lens.  Place  the  lens  a  distance  from  a  white  wall  about 
equal  to  its  focal  length.  Place  a  candle  flame  (better  the  flame  of 
a  fish-tail  burner)  at  such  a  distance  the  other  side  of  the  lens  that  it 
will  produce  a  distinct  and  well-defined  image  on  the  wall  (Fig.  281). 

(1)  Observe  and  note  on  paper  the  size  and  kind  of  image.     Advance 
the  flame  toward  the  lens,  regulating  at  the  same  time  the  distance 
between  the  lens  and  wall,  so  as  to  preserve  a  distinctness  of  image. 

(2)  Note  the  changes  which  the  image  undergoes.     (3)  When  the 
image  and  flame  become  of  the  same  size,  measure  and  note  the  dis- 
tances of  each  from  the  lens.     (4)  Advance  the  flame  still  nearer, 
and  note  the  changes  in  the  image,  until  it  is  impossible  to  obtain  an 
image  on  the  wall.     Measure  the  distance  of  the  flame  from  the  lens, 
and  compare  this  distance  with  the  focal  length  of  the  lens.     (5)  Move 


PKISMS   AND  LENSES. 


311 


the  flame  still  nearer.     Note  whether  the  rays,  after  emerging  from 
the  lens,  are  divergent  or  convergent.     (6)  See  whether  an  image  and 


Fig.  381. 

an  object  may  change  places.  (7)  Form  images  of  the  flame  on  the 
wall  at  different  distances  from  the  lens ;  measure  the  distances,  also 
the  linear  dimensions  (e.g.  the  width,  or  the  vertical  hight)  of  the 
images,  and  determine  whether  the  linear  dimensions  of  images  are  pro- 
portional to  their  distances  from  the  lens. 

29O.  To  Construct  the  linage  Formed  by  a  Convex 
Lens.  —  Given 
the  lens  L  (Fig. 
282),  whose  prin- 
cipal focus  is  at 
F  (or  F',  for  rays 
coming  from  the 
other  direction), 
and  object  AB  in 
front  of  it;  any 
two  of  the  many 
rays  from  A  will 
determine  where 

its  image  a  is  formed.  The  two  that  can  be  traced  easily  are,  the  one 
along  the  secondary  axis  AOa,  and  the  one  parallel  to  the  principal 
axis  AA' :  the  latter  will  be  deviated  so  as  to  pass  through  the  principal 


312 


RADIANT  ENERGY. 


focus  F,  and  will  afterward  intersect  the  principal  axis  at  some  point  a ; 
so  this  is  the  conjugate  focus  of  A ;  similarly  for  B,  and  all  intermediate 
points  along  the  arrow.  Thus,  a  real  inverted  image  is  formed  at  ab. 


Fig.  883. 

291.  Virtual  Images ;  Simple  Microscope.  —  Since 
rays  that  emanate  from  a  point  nearer  the  lens  than  the 
principal  focus  diverge  after  egress,  it  is  evident  that  their 
focus  must  be  virtual  and  on  the  same  side  of  the  lens  as 
the  object.  Hence,  the  image  of  an  object  placed  nearer 

the  lens  than  the 
principal  focus 
is  virtual,  mag- 
nified, and  erect, 
as  shown  in 
Figure  283.  A 
convex  lens 
Fig. 884.  used  in  this 

manner  is  called  a  simple  microscope. 

Since  the  effect  of  concave  lenses  is  to  scatter  transmitted 
rays,  pencils  of  rays  emitted  from  A  and  B  (Fig.  284), 
after  refraction,  diverge  as  if  they  came  from  Ar  and  B', 
and  the  image  will  appear  to  be  at  A  B'.  Hence,  images 
formed  by  concave  lenses  are  virtual,  erect,  and  smaller  than 
the  object. 


PRISMS   AND   LENSES.  313 

292.  Spherical  Aberration.  —  In  all  ordinary  convex 
lenses  the  curved  surfaces  are  spherical,  and  the  angles 
which  incident  rays  make  with  the  little  plane  surfaces,  of 
which  we  may  imagine  the  spherical  surface  to  be  made 


Fig.  285. 

up,  increase  rapidly  toward  the  edge  of  the  lens.  Thus, 
while  those  rays  from  a  given  point  of  an  object,  as  A 
(Fig.  285),  which  pass  through  the  central  portion,  meet 
approximately  at  the  same  point  F,  those  which  pass 
through  the  marginal  portion  are  deviated  so  much  that 
they  cross  the  axis  at  nearer  points,  e.g.  at  F' ;  so  a  blurred 
image  results.  This  wandering  of  the  rays  from  a  single 
focus  is  called  spherical  aberration.  The  evil  may  be 
largely  corrected  by  interposing  a  diaphragm  DD',  pro- 
vided with  a  central  aperture,  smaller  than  the  lens,  so 
as  to  obstruct  those  rays  that  pass  through  the  marginal 
part  of  the  lens. 

Experiment  254.  —  (illustrating  spherical  aberration.)  Cut  a 
cardboard  disk  as  large  as  the  convex  lens  (Fig.  280).  Cut  a  ring  of 
holes  near  the  circumference,  and  also  a  ring  near  the  center.  Sup- 
port the  disk  close  to  the  lens,  so  as  to  cover  one  of  its  surfaces. 
Place  the  whole  in  a  beam  from  a  porte  lumiere.  Catch  refracted 
beams  on  a  screen.  Move  the  screen  aw  ay  from  the  lens.  The  beams 
through  the  outer  ring  of  spots  are  the  first  to  cross  one  another  and 
form  an  image.  Further  away,  the  inner  beams  coincide,  forming  an 
image.  The  outer  ones  having  crossed,  form  a  ring  of  spots. 


314 


RADIANT   ENERGY. 


,  Section  VII. 

PRISMATIC   ANALYSIS   OF   LIGHT-WA1 


293.  Analysis  of  Light- Waves  which  Produce  the 
Sensation  of  White. 

Experiment  255.  —  Place  the  disk  with  adjustable  slit  in  the  aper- 
ture of  a  porte  lumiere,  so  as  to  exclude  all  light-waves  from  a  darkened 
room  except  those  which  pass  through  the  slit.  Near  the  slit  inter- 
pose a  double-convex  lens  of  (say)  10-inch  focus.  A  narrow  sheet  of 
light  will  traverse  the  room  and  produce  an  image  AB  (Fig.  286)  of 
the  slit  on  a  white  screen  placed  in  its  path.  Now  place  a  glass  prism 
C  in  the  path  of  the  narrow  sheet  of  light-waves  and  near  to  the  lens 
with  its  edare  vertical.  (1)  The  light-waves  now  are  not  only  turned 


Fig.  286. 


from  their  former  path,  but  that  which  before  was  a  narrow  sheet,  is, 
after  emerging  from  the  prism,  spread  out  fan-like  into  a  wedge-shaped 
body,  with  its  thickest  part  resting  on  the  screen.  (2)  The  image, 
before  only  a  narrow,  vertical  band,  is  now  drawn  out  into  a  long 


PRISMATIC   ANALYSIS   OF   LIGHT-WAVES.  315 

horizontal  ribbon,  DE.  (3)  The  image,  before  white,  now  presents  all 
the  colors  of  the  rainbow,  from  red  at  one  end  to  violet  at  the  other ; 
it  passes  gradually  through  all  the  gradations  of  red,  orange,  yellow, 
green,  blue,  and  violet.  (The  difference  in  deviation  between  the  red 
and  the  violet  is  purposely  much  exaggerated  in  the  figure.) 

From  this  experiment  we  learn  (1)  that  white  waves  (i.e. 
those  waves  which  are  capable  of  producing  the  sensation 
of  white)  are  not  simple  in  their  composition,  but  the  result 
of  a  mixture.  (2)  The  color  waves  of  which  white  waves  are 
composed  may  be  separated  by  refraction.  (3)  The  cause  of 
the  separation  is  due  to  the  different  degrees  of  deviation 
which  they  undergo  by  refraction.  Red  waves,  which  are 
always  least  turned  aside  from  a  straight  path,  are  the 
least  refrangible.  Then  follow  orange,  yellow,  green,  blue, 
and  violet  in  the  order  of  their  refrangibility.  The  many- 
colored  ribbon  DE  is  called  the  solar  spectrum.  This 
separation  of  white  waves  into  their  constituents  is  called 
dispersion.  The  variety  of  color  waves  of  which  white 
waves  are  composed  is  really  infinite ;  but  we  name  the 
seven  principal  ones  as  follows:  rqd,  orange  (or  citron), 
yellow,  green,  c$axi-blue,  ultramarine-blue^  and  violet;  these 
are  called  the  prismatic  colors.  The  names  of  the  blues 
are  derived  from  the  names  of  the  pigments  which  most 
closely  resemble  them. 

294.  The  Rainbow. — The  rainbow  is  an  illustration  of  a  solar 
spectrum  on  a  grand  scale.  It  is  the  result  of  refraction,  reflection,  and  dis- 
persion of  sunlight  by  falling  raindrops.  Let  spheres  1  and  2  (Fig.  287) 
represent  drops  at  the  extreme  opposite  edges  of  the  bow.  The  eye  is  in  a 
position  to  receive  after  the  dispersion  and  internal  reflection  of  the  light- 
waves within  this  drop,  only  the  red  waves ;  consequently  this  part  of  the 
bow  appears  red.  So,  likewise,  from  drop  2,  the  eye  receives  only  violet ; 
consequently  this  edge  appears  violet.  In  like  manner,  the  intermediate 
colors  of  the  bow  are  sifted  out. 

Outside  the  primary  bow  a  secondary  bow  (Fig.  288)  is  sometimes  seen. 
Drops  3  and  4  (Fig.  287)  are  supposed  to  be  at  the  opposite  edges  of  the 


316 


RADIANT   ENERGY. 


Fig.  387. 

secondary  bow.  It  will  be  seen  that  the  light-waves  undergo  two  internal 
reflections  within  the  drops  which  produce  this  bow.  The  colors  of  this 
bow  are  in  reverse  order  of  those  of  the  primary  bow,  and  less  brilliant. 


Fig.  388. 

295.  Synthesis  of  White  Waves.  —  The  composition 
of  white  waves  has  been  ascertained  by  the  process  of  anal- 
ysis ;  can  it  be  verified  by  synthesis  ?  —  i.e.  can  the  colors 


PRISMATIC   ANALYSIS   OF   LIGHT-WAVES.  317 

after  dispersion  be  reunited  ?  and,  if  so,  will  white  be  re- 
stored ? 

Experiment  256.  —  Place  a  second  prism  (2)  in  such  a  position 
(Z$7)  that  light-waves  which  have  passed  through  one  prism  (1),  and 
been  refracted  and  decomposed,  may  be  refracted  back,  and  the  colors 
\v  ill  be  reblended,  and  a  white  image  of  the  slit  will  be  restored  on 
the  screen. 

Experiment  257.  —  Place  a  large  convex  lens,  or  a  concave  mirror, 
so  as  to  receive  the  colors  after  dispersion  by  a  prism,  and  bring  the  rays 
to  a  focus  on  a  screen.  The  image  produced  will  be  white. 

296.  Cause  of  Color  Revealed  by  Dispersion.  —  Color 
is  determined  solely  by  the  number  of  waves  emitted  by  a 
luminous  body  in  a  second  of  time,  or  by  the  corresponding 
wave-length.  In  a  dense  medium,  the  short  waves  are  more 
retarded  than  the  longer  ones ;  hence  they  are  more  re- 
fracted. This  is  the  cause  of  dispersion.  The  ether  waves 
diminish  in  length  from  the  red  to  the  violet.  As  pitch 
depends  on  the  number  of  aerial  waves  which  strike  the 
ear  in  a  second,  so  color  depends  on  the  number  of  ethereal 
waves  which  strike  the  eye  in  a  second. 

From  well-established  data,  determined  by  a  variety  of  methods  (see 
larger  works),  physicists  have  calculated  the  number  of  waves  that  suc- 
ceed one  another  for  each  of  the  several  prismatic  colors,  and  the  corre- 
sponding wave-lengths ;  the  following  table  contains  the  results.  The  let- 
ters A,  C,  D,  etc.,  refer  to  Fraunhofer's  lines  (see  Plate  I.). 

Length  of  waves  Number  of  waves 

in  millimeters.  per  second. 

Dark  red A 000760 395,000,000,000,000 

Orange C ,  ..     .000656 458,000,000,000,000 

Yellow D 000589 510,000,000,000,000 

Green E .000527 570,000,000,000,000 

C.  Blue F 000486 618,000,000,000,000 

U.  Blue G 000431 697,000,000,000,000 

Violet H . . , 000397 760,000,000,000,000 

There  is  a  limit  to  the  sensibility  of  the  eye  as  well  as  of  the  ear.  The 
limit  in  the  number  of  vibrations  appreciable  by  the  eye  lies  approximately 


318  RADIANT    ENERGY. 

within  the  range  of  numbers  given  in  the  above  table ;  i.e.  if  the  succes- 
sion of  waves  is  much  more  or  less  rapid  than  indicated  by  these  numbers, 
they  do  not  produce  the  sensation  of  sight. 

297.  Continuous    Spectra.  —  All  luminous  solids  and 
liquids   give  continuous  spectra.      If  the  spectrum  is   not 
complete,  as  when  the  temperature  is  too  low,  it  will  begin 
with  red,  and  be  continuous  as  far  as  it  goes. 

298.  Spectroscope.  —  A  small  instrument  called  a  pocket  spectro- 
scope l  will  answer  for  all  experiments  given  in  this  book.     More  elaborate 
experiments  require   more   elaborate   apparatus,  a  description  of  which 
must  be  sought  for  in  larger  works  on  this  subject.     This  instrument  con- 
tains three  or  more  prisms,  A,  B,  and  C  (Fig.  289).     The  prisms  are  en- 
closed in  a  brass  tube  D,  and  this  tube  in  another  tube  E.     F  is  a  convex 
lens,  and  G  is  an  adjustable  slit.     By  moving  the  inner  tube  back  and 
forth,  the  instrument  may  be  so  focused  that  parallel  rays  will  fall  upon 


Fig.  289. 

prism  A.  By  varying  the  kind  of  glass  used  in  the  different  prisms,2  as 
well  as  their  structure,  the  deviation  of  light-waves  from  a  straight  path, 
in  passing  through  them,  is  overcome,  while  the  dispersion  is  preserved. 
On  account  of  the  directness  of  the  path  of  light-waves  through  it,  this 
instrument  is  called  a  direct-vision  spectroscope. 

299.    Bright  lane,  Absorption,  or  Reversed  Spectra. 

Experiment  258.  —  Open  the  slit  about  one-sixteenth  of  an  inch 
wide,  by  turning  the  milled  ring  M  (Fig. 
290),  and  look  through  the  spectroscope  at 
the  sky  (not  at  the  sun,  for  its  light-waves 
are  too  intense  for  the  eye),  and  you  will  see 

Fig.  290.  J    "  J 

a  continuous  spectrum. 

llt  is  expected  that  the  pupil  will  be  provided  with  a  pocket  spectroscope,  the  cost  of 
which  need  not  exceed  ten  dollars. 

2  A  and  C  are  crown-glass,  and  B  is  flint-glaec. 


PRISMATIC   ANALYSIS   OF   LIGHT-WAVES.  319 

Experiment  259.  —  Repeat  the  last  experiment  with  a  candle, 
kerosene,  or  ordinary  gas  flame,  and  you  will  obtain  similar  results. 

Experiment  260.  —  Take  a  piece  of  platinum  wire  16  inches  long. 
Seal  one  end  by  fusion  to  a  short  glass  tube  for  a  handle.  Bend  the 
wire  at  a  right  angle.  Dip  a  portion  of  the  wire  into  a  strong  solution 
of  common  salt,  and  support  it  by  a  clamp  in  the  midst  of  the  almost 
invisible  and  colorless  flame  of  a  Bunsen  burner  or 
alcohol  lamp  (Fig.  291).  Instantly  the  flame  becomes 
luminous  and  colored  a  deep  yellow.  Examine  it  with 
a  spectroscope,  and  you  will  find,  instead  of  a  continuous 
spectrum  beginning  with  red,  only  a  bright,  narrow 
line  of  yellow,  in  the  yellow  part  of  the  spectrum,  next 
the  orange.  Your  spectrum  consists  essentially  of  a 
single  bright  yellow  line  on  a  comparatively  dark 

j    ,          o    j-  TO    j.      T     c        x-      •        x  Fig.  291. 

ground  (see  Sodium,  Hate  I.,  frontispiece). 

Experiment  261.  —  Heat  the  platinum  wire  until  it  ceases  to  color 
the  flame,  then  dip  it  into  a  solution  of  chloride  of  lithium,  and  repeat 
the  last  experiment.  You  obtain  a  carmine-tinted  flame,  and  see 
through  the  spectroscope  a  bright  red  line  and  a  faint  orange  line 
(see  Lithium,  Plate  I.). 

Experiment  262.  —  Use  potassium  hydrate,  and  you  obtain  a 
violet-colored  flame,  and  a  spectrum  consisting  of  a  red  line  and  a 
violet  line  (the  latter  is  very  difficult  to  see  even  with  the  best  instru- 
ments). Use  strontium  nitrate,  and  obtain  a  crimson  flame,  and  a 
spectrum  consisting  of  several  lines  in  the  red  and  the  orange,  and  a 
blue  line  (see  Potassium  and  Strontium,  Plate  I.). 

Experiment  263.  —  Use  a  mixture  of  several  of  the  above  chemi- 
cals, and  you  will  obtain  a  spectrum  containing  all  the  lines  that  char- 
acterize the  several  substances. 

Every  chemical  compound  used  in  the  above  experiments 
contains  a  different  metal,  e.g.  common  salt  contains  the 
metal  sodium  ;  the  other  substances  used  successively  con- 
tain respectively  the  metals  lithium,  potassium,  and  stron- 
tium. These  metals,  when  introduced  into  the  flame,  are 
vaporized,  and  we  get  their  spectra  when  in  a  gaseous 
state.  All  incandescent  gases,  unless  under  great  pressure, 
give  discontinuous,  or  bright  line,  spectra,  and  no  two  gases 
give  the  same  spectra. 


320  RADIANT   ENERGY. 

3OO.    Dark-line  Spectra. 

Experiment  264.  —  Close  the  slit  of  the  spectroscope  so  that  the 
aperture  will  be  very  narrow;  direct  it  once  more  to  the  sky,  and 
slowly  move  the  inner  tube  back  and  forth,  and  you  will  find,  with  a 
certain  suitable  adjustment  which  may  be  obtained  by  patient  trial, 
that  the  solar  spectrum  is  not  in  reality  continuous,  but  is  crossed  by 
several  dark  lines  (see  Solar  Spectrum,  Plate  I.). 

Remark.  —  In  general  it  is  best  to  focus  either  the  D  line  in  the  orange, 
or  the  E  line  in  the  green.  The  inner  sliding  tube  ought  to  be  drawn  out 
a  little  when  examining  the  blue  end  of  the  spectrum,  and  pushed  in  for 
focusing  the  lines  in  the  red. 

Experiment  265.  —  Put  a  few  copper  turnings  in  a  test-tube,  add 
a  little  nitric  acid.  Hold  the  tube  causing  the  colored  vapor  before 
the  slit,  and  notice  the  black  bands. 

Experiment  266.  —  The  electric  light  is  now  in  so  common  use 
that  it  may  be  possible  to  perform  this  experiment.  Between  the 
electric  light  and  the  spectroscope  introduce  the  flame  of  a  Bunsen 
burner,  and  color  it  yellow  with  salt.  Examine  the  spectrum  formed 
through  this  yellow  flame. 

In  the  last  experiment  you  would  naturally  expect  to 
find  the  yellow  part  of  the  spectrum  uncommonly  bright, 
for  there  would  apparently  be  added  to  the  yellow  waves 
of  the  electric  light  the  yellow  waves  of  the  salted  flame. 
But  precisely  where  you  would  look  for  the  brightest 
yellow,  there  you  discover  that  the  spectrum  is  crossed 
by  a  dark  line.  If  you  use  salts  of  lithium,  potassium, 
and  strontium  in  a  similar  mariner,  you  will  find  in  every 
case  your  spectrum  crossed  by  dark  lines  where  you  would 
expect  to  find  bright  lines.  Remove  the  Bunsen  flame, 
and  the  dark  lines  disappear.  It  thus  appears  that  the 
vapors  of  different  substances  absorb  or  quench  the  very 
same  waves  that  they  are  capable  of  emitting ;  very  much, 
it  would  seem,  as  a  given  tuning-fork  selects  from  various 
sound-waves  only  those  of  a  definite  length  corresponding 


PRISMATIC   ANALYSIS   OF   LIGHT-WAVES.  321 

to  its  own  vibration-period.  The  dark  places  of  the  spec- 
trum are  illuminated  by  the  salted  flame ;  but  these  places 
are  so  feebly  illuminated  in  comparison  with  those  places 
illuminated  by  the  electric  light,  that  the  former  appear 
dark  by  contrast.  Light-waves  transmitted  through  cer- 
tain liquids  (as  sulphate  of  quinine  and  blood)  and  certain 
solids  (as  some  colored  glasses)  produce  dark-line  spectra. 
These  spectra  are  obtained  only  when  light-waves  pass 
through  media  capable  of  absorbing  waves  of  certain 
length;  hence  they  are  commonly  called  absorption  spec- 
tra. Since  a  given  vapor  causes  dark  lines  precisely  where, 
if  it  were  itself  the  only  radiator  of  light-waves,  it  would 
cause  bright  lines,  dark-line  spectra  are  frequently  called 
reversed  spectra.  There  are  then  three  kinds  of  spectra: 
continuous  spectra,  produced  by  luminous  solids,  liquids, 
or,  as  has  been  found  in  a  few  instances,  gases  under  great 
pressure ;  bright-line  spectra,  produced  by  luminous  vapors ; 
and  absorption  spectra,  produced  by  light-waves  that  have 
been  sifted  by  certain  media. 

3O1*  Spectrum  Analysis.  —  More  elaborate  spectroscopes  contain 
many  prisms,  by  which  the  purity  of  the  spectrum  is  greatly  increased. 
(By  purity  is  meant  a  freedom  from  the  overlapping  of  images  of  the  slit, 
by  which  many  lines  of  the  spectrum  are  obscured.)  They  also  contain  an 
illuminated  scale  which  may  be  seen  adjacent  to  the  spectrum,  by  which  the 
exact  position  of  the  lines  and  their  relative  distances  from  one  another 
can  be  accurately  determined,  and  a  telescope  by  which  the  spectrum  and 
scale  may  be  magnified.  The  positions  of  some  of  the  prominent  lines  of 
the  solar  spectrum  were  first  determined,  mapped,  and  distinguished  from 
one  another  by  certain  letters  of  the  alphabet,  by  Fraunhofer;  hence  the 
dark  lines  of  the  solar  spectrum  are  commonly  called  Fraunhofer's  lines. 
So  far  as  discovered,  no  two  substances  have  a  spectrum  consisting  of  the 
same  combination  of  lines  ;  and,  in  general,  different  substances  but  very 
rarely  possess  lines  appearing  to  be  common  to  both.  Hence,  when  we  have 
once  observed  and  mapped  the  spectrum  of  any  substance,  we  may  ever 
after  be  able  to  recognize  the  presence  of  that  substance  when  emitting 
light-waves,  whether  it  is  in  our  laboratory  or  in  a  distant  heavenly  body. 


322  RADIANT  ENERGY. 

The  spectroscope,  therefore,  furnishes  us  a  most  efficient  means  of  detect- 
ing the  presence  (or  absence)  of  any  elementary  substance,  even  when 
it  is  combined  or  mixed  with  other  substances.  It  is  not  necessary  that 
the  given  substance  should  exist  in  large  quantities;  for  example,  a 
fourteen-millionth  of  a  milligram  of  sodium  can  be  detected  by  the  spec- 
troscope. 

302.  Celestial  Chemistry  and  Physics.  — The  spectrum  of 
iron  has  been  mapped  to  the  extent  of  460  bright  lines.     The  solar  spec- 
trum furnishes  dark  lines  corresponding  to  nearly  all  these  bright  lines. 
Can  there  be  any  doubt  of  the  existence  of  iron  in  the  sun  ?     By  exami- 
nation of  the  reversed  spectrum   of  the   sun,  we   are  able  to  determine 
with    certainty    the    existence    there  of    sodium,  calcium,  copper,    zinc, 
magnesium,  hydrogen,  and   many  other  known  substances.      The  moon 
and  other  heavenly  bodies  that  are  visible  only  by  reflected  sunlight  give 
the  same  spectra  as  the  sun,  while  those  that  are  self-luminous  give  spectra 
which  differ  from  the  solar  spectrum. 

303.  Relative    Heating    and    Chemical    Effects    of 
Ether- Waves  of  Different  Lengths.  —  If  a  sensitive  thermome- 
ter is  placed  in  different  parts  of  the  solar  spectrum,  it  will  indicate  heat  in 
all  parts ;  but  the  heat  generally  increases  from  the  violet  toward  the  red. 
It  does  not  cease,  however,  with  the  limit  of  the  visible  spectrum ;  indeed, 
if  the  prism  is  made  of  flint  glass,  the  greatest  heat  is  just  beyond  the  red. 
A  strip  of  paper  wet  with  a  solution  of  chloride  of  silver  suffers  no  change  in 
the  dark ;  in  the  light-waves  it  quickly  turns  black ;  exposed  to  the  light- 
waves of  the  solar  spectrum,  it  turns  dark,  but  quite  unevenly.    The  change 
is  slowest  in  the  red,  and  constantly  increases,  till  about  the  region  indicated 
by  G  (see  Solar  Spectrum,  Plate  I.),  where  it  attains  its  maximum ;  from 
this  point  it  falls  off,  and  ceases  at  a  point  considerably  beyond  the  limit  of 
the  violet.     It  thus  appears  that  the  solar  spectrum  is  not  limited  to  the 
visible  spectrum,  but  extends  beyond  at  each  extremity.     Those  waves 
that  are  beyond  the  red  are  usually  called  the  infra-red  waves,  while  those 
that  are  beyond  the  violet  are  called  the  ultra-violet  waves.     The  infra-red 
waves  are  of  longer  vibration-period,  and  the  ultra-violet  of  shorter  period, 
than  the  light-waves. 

304.  Only  one  Kind  of  Radiation.  —  It  has  been  shown  that 
radiant  energy  may  produce  three  distinct  effects,  according  to  the  means 
by  which  it  is  absorbed  or  the  sense  which  it  affects.     But  the  radiant 
energy  producing  these  three  and  other  effects  is  but  one  and  the  same 
thing.     The  only  difference  in  radiant  energy  is  that  which  is  common  to 


PRISMATIC   ANALYSIS   OF   LIGHT-WAVES.  323 

all  wave-motion,  viz.  difference  in  wave-length  and  difference  in  amplitude, 
the  latter  causing  the  wave  to  possess  more  energy  as  the  amplitude  is 
greater.  By  a  lamp-blacked  surface  nearly  all  the  radiant  energy  of  waves 
of  whatever  length  is  absorbed  and  transformed  into  heat.  By  exposing 
such  a  surface  to  spectra  we  learn  that  the  longer  waves  possess  more 
energy  than  the  shorter.  On  the  other  hand,  most  chemical  mixtures  which 
are  affected  by  sunlight  are  more  sensitive  to  the  shorter  waves,  i.e.  this 
rate  of  vibration  stimulates  chemical  action  to  a  greater  extent.  But  the 
sense  of  sight  is  affected  only  by  waves  within  the  range  already  stated, 
§  297. 

While  waves  traverse  the  ether  there  is  neither  heat  nor  light  (i.e. 
sensation)  ;  hence  the  propriety  of  applying  either  of  these  terms  to  a 
train  of  waves  traversing  the  ether  may  well  be  called  in  question.  Yet 
this  is  all  that  traverses  the  space  between  the  sun  and  the  earth. 

3O5.  Chromatic  Aberration.  —  There  is  a  serious  de- 
fect in  ordinary  convex  lenses,  to  which  we  have  not  before 
alluded,  called  chromatic  aberration,  which  has  required 
the  highest  skill  to  correct.  The  convex  lens  both  re- 
fracts and  disperses  the  light-waves  that  pass  through  it. 
The  tendency,  of  course,  is  to  bring  the  more  refrangible 
rays,  as  the  violet,  to  a  focus  much  sooner  than  the  less 
refrangible  rays,  such  as  the  red.  The  result  is  a  disagree- 
able coloration  of  the  images  that  are  formed  by  the  lens, 
especially  by  that  portion  of  the  light-waves  that  passes 
through  the  lens  near  its  edges.  This  evil  has  been 
overcome  very  effectually  by  combining  with  the 
convex  lens  a  plano-concave  lens.  Now,  if  a  crown- 
glass  convex  lens  is  taken,  a  flint-glass  concave 
lens  may  be  prepared  that  will  correct  the  disper- 
sion of  the  former  without  neutralizing  all  its 
refraction.1  A  compound  lens,  composed  of  these  two 
lenses  (Fig.  292)  cemented  together,  constitutes  what  is 
called  an  achromatic  lens. 

1  The  refractive  and  dispersive  powers  of  the  two  lenses  are  not  proportional. 


324  RADIANT   ENERGY. 

Section  VIII. 

COLOR. 

3O6.  Cojor  Produced  by  Absorption.  —  "Color  is  a 
sensation"  [Alfred  Daniell].  "All  objects  are  black  in 
the  dark  "  ;  this  is  equivalent  to  saying  that  without  light- 
waves there  is  no  color.  Is  color  due  to  some  quality  of  an 
object,  or  is  it  due  to  a  quality  of  the  light-waves  which 
illuminate  the  object  ? 

Experiment  267.  —  We  have  found  that  common  salt  introduced 
into  a  Bunsen  flame  renders  it  luminous,  and  that  the  light-waves,  when 
analyzed  with  a  prism,  is  found  to  contain  only  yellow.  Expose  papers 
or  fabrics  of  various  colors  to  these  light-waves  in  a  darkened  room. 
No  one  of  them  exhibits  its  natural  color,  except  yellow. 

Experiment  268.  —  Hold  a  narrow  strip  of  red  paper  or  ribbon  in 
the  red  portion  of  the  solar  spectrum ;  it  appears  red.  Slowly  move 
it  toward  the  other  end  of  the  spectrum ;  on  leaving  the  red  it  be- 
comes darker,  and  when  it  reaches  the  green  it  is  quite  black,  or 
colorless,  and  remains  so  as  it  passes  the  other  colors  of  the  spectrum. 
Repeat  the  experiment,  using  other  colors,  and  notice  that  only  in 
light-waves  of  its  own  color  does  each  strip  of  paper  appear  of  its 
color ;  while  in  all  other  colors  it  is  dark. 

These  experiments  show  that  (I/)  color  is  due  to  a  quality 
of  the  light-ivaves  which  illuminate,  and  not  of  the  object 
illuminated,  though  by  a  conventionality  of  language  we 
ascribe  colors  to  objects;  (2)  in  order  that  an  object  may 
appear  of  a  certain  color,  it  must  receive  light-waves  of  that 
color ;  and  of  course  if  it  receives  other  color  waves  at  the 
same  time,  it  must  be  capable  of  absorbing  or  transmitting 
them.  The  energy  of  the  waves  absorbed  is  converted  into 
heat,  and  warms  the  object.  When  white  waves  (i.e.  those 
capable  of  producing  the  sensation  of  white)  strike  an 


COLOR.  325 

object,  it  appears  white  if  it  reflects  all  the  color  waves.  If 
red  waves  fall  upon  the  same  object,  it  appears  red,  for  it 
is  capable  of  reflecting  red  waves ;  or  it  appears  green,  if 
green  waves  alone  fall  on  it.  If  white  waves  fall  upon 
an  object,  and  all  the  color  waves  are  absorbed  except  the 
blue,  the  object  appears  blue.  When  we  paint  our  houses 
we  do  not  apply  color  to  them.  We  apply  substances, 
called  pigments,  that  have  a  property  of  absorbing  all  the 
color  waves  except  those  which  we  would  have  our  houses 
appear. 

Experiment  269.  —  By  means  of  a  porte  lumiere  introduce  a  beam 
into  a  dark  room.  Cover  the  orifice  with  a  deep  red  (copper)  glass. 
The  white  waves,  in  passing  through  the  glass,  appear  to  be  colored 
red.  Does  the  glass  color  the  waves  red  ? 

Experiment  270.  —  With  the  slit,  lens,  and  prism  form  a  solar 
spectrum,  and  between  the  prism  and  screen  interpose  the  red  glass. 
Very  few  light-waves,  except  the  red,  are  transmitted;  the  rest  are 
absorbed  by  the  glass. 

It  thus  appears  that  a  red  transparent  body  is  red  becauso 
it  transmits  few  light-waves  except  the  red,  not  because  the 
body  colors  the  waves. 

3D  7.    Sky  Colors. 

Experiment  271.  —  Dissolve  a  little  white  castile  soap  in  a  tum- 
bler of  water ;  or,  better,  stir  into  the  water  a  few  drops  of  an  alcoholic 
solution  of  mastic,  enough  to  render  the  water  slightly  turbid.  Place 
a  black  screen  behind  the  tumbler,  and  examine  the  liquid  by  reflected 
sunlight,  —  the  liquid  appears  to  be  blue.  Examine  the  liquid  by 
transmitted  sunlight,  —  it  now  appears  yellowish  red. 

Sky-light  is  the  result  of  reflected  light-waves.  The  particles  of  atmos- 
pheric dust  (of  water,  probably)  that  pervade  the  atmosphere,  like  the  fine 
particles  of  mastic  suspended  in  the  water,  reflect  blue  light-waves  ;  while 
beyond  the  atmosphere  is  a  black  background  of  darkness.  But  we  must 
not,  from  this,  conclude  that  the  atmosphere  is  blue ;  for,  unlike  blue 
glass,  but  like  the  turbid  liquid,  it  transmits  yellow  and  red  rays  freely, 


326  RADIANT  ENERGY. 

so  that,  seen  by  reflected  light-waves,  it  is  blue,  but  seen  by  transmitted 
light-waves  it  is  yellowish  red. 

Experiment  272.  — Pour  some  of  the  turbid  liquid  into  a  small 
test-tube,  and  examine  it  and  the  tumbler  of  liquid  by  transmitted 
light-waves;  the  former  appears  almost  colorless,  while  the  latter  is 
quite  deeply  colored. 

When  the  sun  is  near  the  horizon,  its  rays  travel  a  greater  distance  in 
the  air  to  reach  the  earth  than  when  it  is  in  the  zenith ;  consequently,  there 
is  a  greater  loss  by  absorption  and  reflection  in  the  former  case  than  in  the 
latter.  But  the  yellow  and  red  rays  suffer  less  destruction,  proportionally, 
than  the  other  colors ;  consequently,  these  colors  predominate  in  the  morn- 
ing and  evening. 

The  remarkable  "  yellow  days  "  of  the  summer  of  1882  are  explained  in 
this  way.  The  atmosphere  on  this  continent  was  remarkably  turbid  dur- 
ing those  days. 

3O8.  Mixing1  Colors.  —  A  mixture  of  all  the  prismatic 
colors,  in  the  proportion  found  in  sunlight,  produces  white. 
Can  white  be  produced  in  any  other  way  ? 

Experiment  273.  — On  a  black  surface  A  (Fig.  293),  about  2 
inches  apart,  lay  two  small  rectangular  pieces  of  paper,  one  yellow 
and  the  other  blue.  In  a  vertical  position  between, 
and  from  2  inches  to  6  inches  above,  these  papers, 
hold  a  slip  of  plate  glass  C.  Looking  obliquely 
down  through  the  glass  you  may  see  the  blue  paper 
by  transmitted  light-waves  and  the  yellow  paper 
by  reflection.  That  is,  you  see  the  object  itself 
in  the  former  case,  and  the  image  of  the  object 
in  the  latter  case.  By  a  little  manipulation,  the 
image  and  the  object  may  be  made  to  overlap 
one  another,  when  both  colors  will  apparently 
disappear,  and  in  their  place  the  color  which  is 
Fig.  293.  the  result  of  the  mixture  will  appear.  In  this 

case  it  will  be  white,  or,  rather,  grayy  which  is  white  of  a  low  degree 
of  luminosity.  If  the  color  is  yellowish,  lower  the  glass ;  if  bluish, 
raise  it. 

Experiment  274.  —  With  the  rotating  apparatus,  rotate  the  disk 
(Fig.  294)  which  contains  only  yellow  and  blue.  The  colors  so  blend 


COLOR.  327 


(i.e.  the  sensations)  in  the  eye  as  to  produce  the  sensation  of  gray,  i.e. 
white  of  low  luminosity. 


Fig.  394.  Fig.  895.  Fig.  296. 

Figure  295  represents  "  Newton's  disk,"  which  contains 
the  seven  prismatic  colors  arranged  in  a  proper  proportion 
to  produce  gray  when  rotated. 

In  like  manner,  you  may  produce  white  by  mixing  pur- 
ple and  green  ;  or,  if  any  color  on  the  circumference  of 
the  circle  (see  Complementary  Colors,  Plate  I.)  is  mixed 
with  the  color  exactly  opposite,  the  resulting  color  will  be 
white.  Again,  the  three  colors,  red,  green,  and  violet, 
arranged  as  in  Figure  296,  with  rather  less  surface  of  the 
green  exposed  than  of  the  other  colors,  will  give  gray. 
Green  mixed  with  red,  in  varying  proportions,  will  produce 
any  of  the  colors  in  a  straight  line  between  these  two 
colors  in  the  diagram  (Plate  I.)  ;  green  mixed  with  violet 
will  produce  any  of  the  colors  between  them ;  and  violet 
mixed  with  red  gives  purple. 

All  colors  are  represented  in  the  spectrum,  except  the  purple  hues.  The 
latter  form  the  connecting  link  between  the  two  ends  of  the  spectrum. 
Our  color  chart  (Plate  I.)  is  intended  to  represent  the  sum  total  of  all  the 
sensations  of  color.  By  means  of  this  chart  we  may  determine  the  result 
of  the  (optical)  mixture  of  any  two  colors  as  follows :  Find  the  places 
occupied  upon  the  chart  by  the  two  colors  which  are  to  be  mixed,  and 
unite  the  two  points  by  a  straight  line.  The  color  produced  by  the  mix- 
ture will  invariably  be  found  at  the  center  of  this  line. 


328  BADIANT  ENERGY. 

3O9.    Mixing  Pigments. 

Experiment  275.  —  Mix  a  little  of  the  two  pigments,  chrome 
yellow  and  ultramarine  blue,  and  you  obtain  a  green  pigment. 

The  last  three  experiments  show  that  mixing  certain 
colors,  and  mixing  pigments  of  the  same  name,  may  pro- 
duce very  different  results.  In  the  first  experiments  you 
mixed  colors;  in  the  last  experiment  you  did  not  mix 
colors,  and  we  must  seek  an  explanation  of  the  result  ob- 
tained. If  a  glass  vessel  with  parallel  sides  containing 
a  blue  solution  of  sulphate  of  copper  is  interposed  in  the 
path  of  the  light-waves  which  form  a  solar  spectrum,  it  will 
be  found  that  the  red,  orange,  and  yellow  waves  are  cut 
out  of  the  spectrum,  i.e.  the  liquid  absorbs  these  waves. 
And  if  a  yellow  solution  of  bichromate  of  potash  is  inter- 
posed, the  blue  and  violet  waves  will  JDC  absorbed.  It 
is  evident  that,  if  both  solutions  are  interposed,  all  the 
colors  will  be  destroyed,  except  the  green,  which  alone 
will  be  transmitted  ;  thus  :  — 


Cancelled  by  the  blue  solution,  G  B  V. 

Cancelled  by  the  yellow  solution,    R  O  Y  G  $  rf. 
Cancelled  by  both  solutions,  $  0  y  G  $  ^. 

In  a  similar  manner,  when  white  waves  strike  a  mixture 
of  yellow  and  blue  pigments  on  the  palette,  they  penetrate 
to  some  depth  into  the  mixture  ;  and,  during  its  passage  in 
and  out,  all  the  colors  are  destroyed,  except  the  green;  so 
the  mixed  pigments  necessarily  appear  green.  But  when 
a  mixture  of  yellow  and  blue  waves  enters  the  eye,  we  get, 
as  the  result  of  the  combined  sensations  produced  by  the 
two  colors,  the  sensation  of  white;  hence  a  mixture  of 
yellow  and  blue  gives  white. 

The  color  square  3  (Plate  I.)  represents  the  result  of  the  mixture  of 
pigments  1  and  2  ;  while  4  represents  the  result  of  the  optical  mixture  of 
the  same  colors. 


COLOR.  329 

31 0.  Complementary  Colors. 

Experiment  276.  —  On  a  piece  of  white,  or  better,  gray,  paper,  lay 
a  circular  piece  of  blue  paper  15mm  in  diameter.  Attach  one  end  of  a 
piece  of  thread  to  the  colored  paper,  and  hold  the  other  end  in  the 
hand.  Place  the  eyes  within  about  15cm  of  the  colored  paper,  and 
look  steadily  at  the  center  of  the  paper  for  about  fifteen  seconds ; 
then,  without  moving  the  eyes,  suddenly  pull  the  colored  paper  away, 
and  instantly  there  will  appear  on  the  gray  paper  an  image  of  the 
colored  paper,  but  the  image  will  appear  to  be  yellow.  This  is 
usually  called  an  after-image.  If  yellow  paper  is  used,  the  color  of  the 
after-image  will  be  blue ;  and  if  any  other  color  given  in  the  diagram 
(Plate  I.),  the  color  of  its  after-image  will  be  the  color  that  stands 
opposite  to  it. 

This  phenomenon  is  explained  as  follows:  When  we 
look  steadily  at  blue  for  a  time,  the  eyes  become  fatigued 
by  this  color,  and  less  susceptible  to  its  influence,  while 
they  are  fully  susceptible  to  the  influence  of  other  colors ; 
so  that  when  they  are  suddenly  brought  to  look  at  white, 
which  is  a  compound  of  yellow  and  blue,  they  receive  a 
vivid  impression  from  the  former,  and  a  feeble  impression 
from  the  latter ;  hence  the  predominant  sensation  is  yellow. 
Any  two  colors  which  together  produce  white  are  said  to 
be  complementary  to  each  other.  The  opposite  colors  in 
the  diagram  (Plate  I.)  are  complementary  to  one  another. 

311.  Effect  of  Constrast.  —  When  any  two  colors  given  in  the 
circle  (Plate  I.)  are  brought  in  contrast,  as  when  they  are  placed  next  one 
another,  the  effect  is  to  move  them  farther  apart.    For  example,  if  red 
and  orange  are  brought  in  contrast,  the  orange  assumes  more  of  a  yellowish 
hue,  and  the  red  more  of  a  purplish  hue.     Colors  that  are  already  as  far 
apart  as  possible,  e.g.  yellow  and  blue,  do  not  change  their  hue,  but  merely 
cause  one  another  to  appear  more  brilliant. 

312.  Color  Produced  by  Interference. 

Experiment  277.  —  In  a  vise  or  other  convenient  instrument, 
press  two  clean  pieces  of  thick  plate  glass  firmly  together.  A  number 
of  colors  will  be  seen  arranged  in  a  certain  order,  and  forming  curves 
more  or  less  regular  around  the  point  of  pressure. 


330 


RADIANT  ENERGY. 


This,  together  with  many  other  kindred  color  phenomena,  is  caused 
by  the  mutual  destruction  by  interference  of  certain  of  the  colors  which 
compose  white,  the  resulting  colors  being  the  product  of  the  combination 
of  those  which  are  not  so  extinguished.  Much  as  certain  over-tones  might 
destroy  one  another,  and  the  quality  of  the  resulting  sound  would  be  deter- 
mined by  the  composition  of  the  surviving  tones. 

Thin,  transparent  films  of  varying  thickness,  such  as  the  film  of  a  soap 
bubble,  are  well  suited  to  show  the  effects  of  interference  of  light-waves. 
Some  of  the  light-waves  which  strike  the  anterior  surface  of  the  film  are 
reflected;  another  portion  enters  the  film,  and  is  reflected  from  the  pos- 
terior surface ;  but,  by  travelling  twice  through  the  film,  the  waves  lose 
ground,  so  that,  on  emergence,  their  phases  may  or  may  not  correspond 
with  the  phases  of  the  former  portion :  this  will  depend  evidently  upon  the 
thickness  of  the  film  at  a  given  point,  and  the  length  of  the  waves  striking 
that  point.  In  this  manner  the  phenomena  obtained  in  the  experiment  are 
explained ;  the  film  in  this  case  is  the  layer  of  air  between  the  two  surfaces 
of  glass. 

Colors  are  produced  by  reflection  from  the  surfaces  of  thin  transparent 
films  of  all  kinds ;  for  example,  the  colors  of  the  soap  bubble,  of  oil  on 
water,  of  the  thin  coating  of  metallic  oxide  formed  in  tempering  steel. 


Section  IX. 

THERMAL  EFFECTS   OF  RADIATION. 

313.  Diathermancy  and  Athermancy. 

Experiment  278.  —  Prepare  a  differential 
thermometer  with  two  glass  flasks  and  a  glass 
tube,  as  represented  in  Figure  297.  Cover  one 
of  the  flasks  with  lamp-black  by  holding  it 
above  a  smoking  kerosene  flame.  Place  colored 
liquid  in  the  bend  A.  Stopper  both  vessels 
tightly  and  expose  the  apparatus  to  the  direct 
rays  of  the  sun.  The  rays  pass  through  the 
clean  glass  and  through  the  air  within,  affecting 
the  temperature  of  either  but  little.  But  the 
lamp-black  absorbs  the  radiations,  the  flask  be- 


THERMAL  EFFECTS   OF   RADIATION.  331 

comes  heated,  the  enclosed  air  becomes  heated  by  contact  with  the 
heated  flask,  the  heated  air  expands  and  pushes  the  liquid  in  the 
tube  toward  the  cooler  flask. 

What  becomes  of  radiations  that  strike  a  body  depends 
largely  upon  the  character  of  the  body.  If  the  nature  of 
the  body  is  such  that  its  molecules  can  accept  the  motion  of 
the  ether,  the  undulations  of  ether  are  said  to  be  absorbed 
by  the  body,  and  the  body  is  thereby  heated ;  that  is,  the 
radiant  energy  is  transformed  into  heat  energy.  A  good 
illustration  of  this  is  the  experiment  with  blackened  glass. 
On  the  other  hand,  the  unblackened  glass  allows  the  radi- 
ations to  pass  freely  through  it,  and  very  little  is  trans- 
formed into  heat.  Notice  how  cold  window-glass  may 
remain,  while  radiations  pour  through  it  and  heat  objects 
within  the  room.  It  must  be  constantly  borne  in  mind 
that  only  those  radiations  that  a  body  absorbs  heat  it ;  those 
that  pass  through  it  do  not  affect  its  temperature.  Bodies 
that  transmit  radiant  energy  freely  are  said  to  be  diather- 
manous, while  those  that  absorb  it  largely  are  called  ather- 
manous.  The  most  diathermanous  solid  is  rock  salt. 
Among  the  most  athermanous  solids  are  lamp-black  and 
alum.  Carbon  bisulphide,  among  liquids,  is  exceptionally 
transparent  to  all  forms  of  radiation  ;  while  water,  trans- 
parent to  short  waves,  absorbs  the  longer  waves,  and  is 
thus  quite  athermanous. 

Dry  air  is  almost  perfectly  diathermanous.  All  of  the  sun's  radiations 
that  reach  the  earth  pass  through  a  layer  of  air  from  fifty  to  two  hundred 
miles  in  depth,  which  contains  a  vast  amount  of  aqueous  vapor.  This 
vapor,  like  water,  is  comparatively  opaque  to  long  waves ;  hence  it  modi- 
fies very  much  the  character  of  the  radiations  which  reach  the  earth.  This 
fact  enables  us  to  understand  the  method  by  which  our  atmosphere  becomes 
heated.  First,  a  very  considerable  portion  of  the  radiant  energy  which 
comes  to  us  from  the  sun,  in  the  form  of  relatively  long  waves,  is  stopped 
by  the  watery  vapor  in  the  air,  which  is,  in  consequence,  heated.  Most  of 


332  RADIANT  ENERGY. 

that  which  escapes  this  absorption  heats  the  earth  by  falling  upon  it.  The 
warmed  earth  loses  its  heat,  —  partly  by  conduction  to  the  air,  still  more 
largely  by  radiation  outward.  The  form  of  radiation,  however,  has  been 
greatly  changed ;  for  now,  coming  from  a  body  at  a  low  temperature,  it  is 
chiefly  in  long  waves  that  the  energy  is  transmitted ;  while,  as  we  have 
seen,  it  was  largely  in  the  form  of  short  waves  that  the  earth  received  its 
heat.  But  it  is  exactly  these  long  waves  which  are  most  readily  stopped 
by  the  atmosphere ;  hence  the  atmosphere,  or  rather  the  aqueous  vapor  of 
the  atmosphere,  acts  as  a  sort  of  trap  for  the  energy  which  comes  to  us 
from  the  sun.  Remove  the  watery  vapor  (which  serves  as  a  "blanket" 
to  the  earth)  from  our  atmosphere,  and  the  chill  resulting  from  the  rapid 
escape  of  heat  by  radiation  would  put  an  end  to  all  animal  and  vegetable 
life.  Glass  does  not  screen  us  from  the  sun's  radiations,  but  it  can  very 
effectually  screen  us  from  the  radiations  from  a  stove  or  any  other  terres- 
trial object.  Glass  is  diathermanous  to  the  sun's  radiations  (simply  because 
they  have  already  lost  most  of  the  very  long  waves  by  atmospheric  absorp- 
tion), but  quite  athermanous  to  other  radiations.  This  is  well  illustrated 
in  the  case  of  hot-beds  and  green-houses.  The  sun's  radiations  pass  through 
the  glass  of  these  enclosures,  almost  unobstructed,  and  heats  the  earth ; 
but  the  radiations  given  out  in  turn  by  the  earth  are  such  as  cannot  pass 
out  through  the  glass ;  hence  the  heat  is  retained  within  the  enclosures. 

314.  All  Bodies  Radiate  Heat.  —  Hot  bodies  usually 
part  with  their  heat  much  more  rapidly  by  radiation  than 
by  all  other  processes  combined.      But  cold  bodies,  like 
ice,  radiate  heat  even  when  surrounded  by  warm  bodies. 
This  must  be  so  from  the  nature  of  the  case,  for  the  mole- 
cules of  the  coldest  bodies  possess  some  motion,  and,  being 
surrounded  by  ether,  they  cannot  move  without  imparting 
some  of  their  motion  to  the  ether,  and  to  that  extent  be- 
come themselves  colder. 

315.  Theory  of  Exchanges. — Let  us  suppose  that  we 
have  two  bodies,  A  and  B,  at  different  temperatures,  A 
warmer  than  B.     Radiation  takes  place  not  only  from  A 
to  B,  but  from  B  to  A ;  but,  in  consequence  of  A's  excess 
of  temperature,  more  radiant  energy  passes  from  A  to 
B  than  from  B  to  A,  and  this  continues  until  both  bodies 


SOME  OPTICAL  INSTRUMENTS.  333 

acquire  the  same  temperature.  At  this  point  radiation  by 
no  means  ceases,  but  each  now  gives  as  much  as  it  receives, 
and  thus  equilibrium  is  kept  up.  This  is  known  as  the 
"  Theory  of  Exchanges." 

316.    Good  Absorbers,  Good  Radiators. 

Experiment  279.  —  Select  two  small  tin  boxes  of  equal  capacity ; 
one  should  be  bright  outside,  while  the  other  should  be  covered  thinly 
with  soot  from  a  candle-flame.  Cut  a  hole  in  the  cover  of  each  box 
large  enough  to  admit  the  bulb  of  a  thermometer.  Fill  both  boxes 
with  hot  water,  and  introduce  into  each  a  thermometer.  They  will 
register  the  same  temperature  at  first.  Set  both  in  a  cool  place,  and 
in  half  an  hour  you  will  find  that  the  thermometer  in  the  blackened 
box  registers  several  degrees  lower  than  the  other.  Then  fill  both 
with  cold  water,  and  set  them  in  front  of  a  fire  or  in  the  sunshine,  and 
it  will  be  found  that  the  temperature  in  the  blackened  box  rises  faster. 

As  bodies  differ  widely  in  their  absorbing  power,  so  they 
do  in  their  radiating  power,  and  it  is  found  to  be  univer- 
sally true  that  good  absorbers  are  good  radiators,  and  bad 
absorbers  are  bad  radiators.  Much,  in  both  cases,  depends 
upon  the  character  of  the  surface  as  well  as  the  substance. 
Bright,  polished  surfaces  are  poor  absorbers  and  poor 
radiators;  while  tarnished,  dark,  and  roughened  surfaces 
absorb  and  radiate  heat  rapidly.  Dark  clothing  absorbs 
radiations  and  radiates  more  rapidly  than  light  clothing. 


Section  X. 

SOME  OPTICAL  INSTRUMENTS. 

317.  Compound  Microscope.  —  The  simple  microscope 
was  described  on  page  312.  When  it  is  desired  to  magnify 
an  object  more  than  can  be  done  conveniently  and  with 


334 


KADIANT   ENERGY. 


distinctness  by  a  single  lens,  two  convex  lenses  are  used, 
—  one  (O,  Fig.  298)  called  the  object-glass,  to  form  a  mag- 
nified real  image  A'B'  of  the  object  AB ;  and  the  other 
(E)  called  the  eye-glass,  to  magnify  this  image  so  that  the 
image  A'B'  appears  of  the  size  A"B". 


Fig.  298. 

Hence  the  compound  microscope  is  virtually  a  simple 
microscope  applied  not  to  the  object,  but  to  its  image 
already  magnified  by  the  object  lens.  Both  lenses  should  be 
achromatic  and  aplanatic  (free  from 
spherical  aberration). 

The  eye-piece  is  made  of  two  or  more 
lenses,  because  it  is  found  that  if  the 
refractions  are  thus  distributed,  the  ex- 
tent of  the  useful  field  may  be  greatly 
increased.  Ordinarily  two  lenses  are 
sufficient. 

The  article  to  be  examined  is  placed 
on  a  glass  stage,  ab  (Fig.  299),  and,  if 
the  object  is  transparent,  it  is  strongly 
illuminated  by  focusing  light  upon  it  by 
means  of  a  concave  mirror,  P.  If  the 


SOME  OPTICAL  INSTRUMENTS. 


335 


object  is  opaque,  it  is  illuminated  by  light-waves  converged 
upon  it  obliquely  from  above  by  a  convex  lens  not  shown 
in  the  figure. 


Fig.  30O. 

318.  Astronomical  Telescope.  —  The  astronomical  re- 
fracting telescope  consists  essentially,  like  the  compound 
microscope,  of  two  lenses.  The  object-glass  (O,  Fig.  300) 
forms  a  real  diminished  image  ab  of  the  object  AB ;  this 
image,  seen  through  the  eye-glass  E,  appears  magnified  and 
of  the  size  cd.  The  object-glass  is  of  large  diameter,  in 
order  to  concentrate  as  much  as  possible  the  radiations  from 
a  distant  object  for  a  better  illumination  of  the  image. 


Fig.  301. 

319.  Photographer's  Camera.  —  The  photographer's 
camera  or  camera  obscura,  of  which  AB  (Fig.  301)  repre- 
sents a  vertical  section,  consists  of  a  dark  box  painted 
black  on  the  interior.  A  screen  of  ground  glass  S  forms 
a  partition  in  the  box.  A  sliding  tube  T  contains  a  con- 


336 


RADIANT  ENERGY. 


vex  lens  L.  If  an  object  D  is  placed  some  distance  in 
front,  ,and  the  distance  of  the  lens  from  the  screen  is  suit- 
ably adjusted,  a  distinct,  real,  and  inverted  image  can  be 
seen  upon  the  screen  by  looking  through  the  aperture  C. 
When  the  image  is  properly  focused,  the  photographer  re- 
places the  ground-glass  plate  by  a  sensitized  plate,  and  the 
chemical  power  of  the  sun's  rays  imprints  a  true  picture 
of  the  object  on  this  plate. 

32O.  The  Human  Eye.  —  Figure  302  represents  a  horizontal 
section  of  this  wonderful  organ.  Covering  the  front  of  the  eye,  like  a 

watch-crystal,  is  a  transparent  coat 
1,  called  the  cornea.  A  tough  mem- 
brane 2,  of  which  the  cornea  is  a  con- 
tinuation, forms  the  outer  wall  of  the 
eye,  and  is  called  the  sclerotic  coat,  or 
' '  white  of  the  eye."  This  coat  is 
lined  on  the  interior  with  a  delicate 
membrane  3,  called  the  choroid  coat; 
the  latter  contains  a  black  pigment, 
which  prevents  internal  reflection. 
The  inmost  coat  4,  called  the  retina, 
is  formed  by  expansion  of  the  optic 
nerve  O.  The  muscular  tissue  ii  is 
called  the  iris;  its  color  determines 
In  the  center  of  the  iris  is  a  circular 
opening  5,  called  the  pupil,  whose  function  is  to  regulate,  by  involuntary 
enlargement  and  contraction,  the  quantity  of  light-waves  admitted  to 
the  anterior  chamber  of  the  eye.  Just  back  of  the  iris  is  a  tough,  elastic, 
and  transparent  body  6,  called  the  crystalline  lens.  This  lens  divides  the  eye 
into  two  chambers ;  the  anterior  chamber  7  is  filled  with  a  limpid  liquid, 
called  the  aqueous  humor ;  the  posterior  chamber  8  is  filled  with  a  jelly-like 
substance,  called  the  vitreous  humor. 

Experiment  280.  —  Make  a  model  of  an  eye.  Fill  an  8-ounce 
flask  with  clear  water  (eye-ball).  Cover  one  side  with  black  paper 
having  a  round  hole  in  it  (iris  and  pupil).  Place  a  slightly  convex 
lens  in  front  of  the  hole  (cornea  and  crystalline  lens  combined ;  the 
latter  outside  the  eye-ball  instead  of  inside).  Place  a  candle  flame 
in  front  of  the  hole  (object)  ;  catch  (inverted)  image  of  the  flame 


Fig.  308. 

the  so-called  "color  of  the  eye." 


SOME  OPTICAL  INSTRUMENTS.  337 

on  a  paper  screen  (retina)  behind  the  flask.  Move  the  candle  a  little 
way  from  the  flask ;  the  image  becomes  indistinct.  Restore  it  by  in- 
terposing another  convex  lens  (cure  of  long  sight).  Bring  the  candle 
near  to  the  flask  till  the  image  is  indistinct.  Interpose  concave  lens 
to  restore  the  clearness  (cure  of  short  sight). 

Experiment  281.  —  Make  two  dots  on  paper  two  inches  apart. 
Close  the  left  eye,  and  bring  the  right  one  over  the  left  spot.  At  a 
distance  of  about  six  inches  the  right  spot  becomes  invisible.  As  you 
bring  the  paper  nearer,  the  eye  turns  to  regard  the  left  spot,  the  image 
of  the  right  spot  meantime  travels  noseward  over  the  retina,  until  it 
reaches  a  spot,  called  the  blind  spot,  on  the  retina,  which  is  not  sensitive 
to  the  action  of  light-waves.  This  spot  is  where  the  optic  nerve  enters 
the  eye. 

The  eye  is  a  camera  obscura,  in  which  the  retina  serves 
as  a  screen.  Images  of  outside  objects  are  projected  by 
means  of  the  crystalline  lens,  assisted  by  the  refractive 
powers  of  the  humors,  upon  this  screen,  and  the  impres- 
sions thereby  made  on  this  delicate  network  of  nerve  fila- 
ments are  conveyed  by  the  optic  nerve  to  the  brain.  If 
the  two  outer  coatings  are  removed  from  the  back  part  of 
the  eye  of  an  ox  recently  killed,  so  as  to  render  it  some- 
what transparent,  true  images  of  whole  landscapes  may  be 
seen  formed  upon  the  retina  of  the  eye,  when  it  is  held  in 
front  of  your  eye.  With  the  ordinary  camera,  the  distance 
of  the  lens  from  the  screen  must  be  regulated  to  adapt 
itself  to  the  varying  distances  of  outside  objects,  in  order 
that  the  images  may  be  properly  focused  on  the  screen.  In 
the  eye  this  is  accomplished  by  changing  the  convexity  of 
the  lens.  We  can  almost  instantly  and  involuntarily 
change  the  lens  of  the  eye,  so  as  to  form  on  the  retina  a 
distinct  image  of  an  object  miles  away  or  only  a  few  inches 
distant.  The  nearest  limit  at  which  an  object  can  be 
placed,  and  form  a  distinct  image  on  the  retina,  is  about 
five  inches.  On  the  other  hand,  the  normal  eye  in  a  pas- 
sive state  is  adjusted  for  objects  at  an  infinite  distance. 


338  KADIANT   ENERGY. 

Curiously  enough,  the  retina,  on  careful  examination,  is 
found  to  be  composed  in  part  of  little  elements  in  its  back 
portion,  which  have  received,  from  their  appearance,  the 
names  of  rods  and  cones.  It  is  thought  that  these  rods 
and  cones  receive  and  respond  to  the  vibrations  of  ether ; 
in  other  words,  that  they  co-vibrate  with  the  undulations 
of  the  ether,  and  thereby  we  get  our  sensation  of  light. 

321.  Stereopticon.  —  This  instrument  is  extensively 
employed  in  the  lecture-room  for  producing  on  a  screen 
magnified  images  of  small,  transparent  pictures  on  glass, 


Fig.  303. 

called  slides  ;  also  for  rendering  a  certain  class  of  experi- 
ments visible  to  a  large  audience  by  projecting  them  on  a 
screen.  The  lime  light  is  most  commonly  used,  though 
the  electric  light  is  preferred  for  a  certain  class  of  pro- 
jections. The  flame  of  an  oxyhydrogen  blow-pipe  A 
(Fig.  303)  is  directed  against  a  stick  of  lime  B,  and  raises 
it  to  a  white  heat.  The  radiations  from  the  lime  are 
condensed,  by  means  of  a  convex  lens  <?,  called  the  con- 
densing lens  (usually  two  plano-convex  lenses  are  used), 
so  that  a  larger  quantity  of  radiations  will  pass  through  the 
convex  lens  E,  called  the  projecting  lens.  The  latter  lens 
produces  (or  projects)  a  real,  inverted,  and  magnified 
image  of  the  picture  on  the  screen  S.  The  mounted  lens 


SOME  OPTICAL  INSTRUMENTS.  339 

E  may  be  slid  back  and  forth  on  the  bar  F,  so  as  properly 
to  focus  the  image.  (For  useful  information  relating  to 
the  operation  of  projection,  see  Dolbear's  Art  of  Projec- 
tion.) 


EXERCISES. 

1.  What  is  light? 

2.  State  points  of  resemblance  and  points  of   difference   between 
light-waves  and  sound-waves.     Which  can  traverse  a  vacuum  (as  re- 
gards matter)  ? 

3.  Two  books  are  held,  respectively,  2  feet  and  7  feet  from  the  same 
gas-flame.     Compare  the  intensities  of  the  illumination  of  their  respec- 
tive pages. 

4.  What  is  the  general  effect  of  a  concave  mirror  on  light-waves  ? 
What  kind  of  lens  produces  a  similar  effect  ? 

5.  How  can  a  beam  be  bent  ? 

6.  State  different  ways  by  which  the  colors  which  compose  white 
light  may  be  revealed. 

7.  How  do  you  account  for  the  color  of  flowers?    How  do  you 
account  for  the  colors  seen  on  a  soap-bubble  ? 

8.  Why  do  white  surfaces  appear  gray  at  twilight  ? 

9.  How  are  objects  heated  by  the  sun  ? 

10.  What  evidences  can  you  give  that  the  earth   receives  energy 
from  the  sun  ? 


APPENDIX. 


Inches. 


Millimeters. 


Centimeters. 


The  area  of  this  figure  is  a  square  decimeter. 
A  cube  of  water,  one  of  whose  sides  is  this  area, 
is  a  cubic  decimeter  or  a  liter  of  water,  and  at  the 
temperature  of  4°  C.  weighs  a  kilogram.  The 
same  volume  of  air  at  0°  C.,  and  under  a  pressure 
•of  one  atmosphere,  weighs  1.293  grams.  The 
gram  is  the  weight  of  I"*  of  pure  water  at  4°  C. 


Square  Inch. 


Square    j 
Centimeter: 


312 


APPENDIX. 


SECTION   A. 

Metric  system  of  measures.  —  The  term  metric  is  derived  from 
the  word  meter,  which  is  the  name  of  the  fundamental  unit  employed 
in  this  system  for  measuring  length,  and  from  which  all  other  units 
of  the  system  are  derived.  The  meter  is,  approximately,  the  ten- 
millionth  part  of  the  distance  from  the  Equator  to  the  North  Pole. 
Defined  by  law,  it  is  the  distance  at  0°  C.  between  two  lines  engraved 
on  a  platinum  bar  kept  in  the  Paris  Observatory.  The  gram  is  theo- 
retically the  mass  of  Ice  of  distilled  water  at  4°  C.  By  law  it  is  y^^ 
of  the  mass  of  a  piece  of  platinum  preserved  in  the  same  observatory. 
At  Washington  are  kept  exact  copies  of  the  meter  and  other  metric 
measures. 

The  following  tables  contain  all  the  requirements  of  this  book.  The 
pupil  will  find  more  complete  tables  in  any  good  arithmetic. 

TABLE  OF  LENGTHS. 

10  millimeters  (mm)  =  1  centimeter  (cm). 
10  centimeters  —  1  decimeter  (dm). 
10  decimeters  =  1  meter  (m). 

1000  meters  =  1  kilometer    1™. 


TABLE    OF    AREAS. 

100  square  millimeters  (q«n»)  =  1  square  centimeter  (***). 
100  square  centimeters  =  1  square  decimeter  (qdm). 

100  square  decimeters  =  1  square  meter  (a01). 

1,000,000  square  meters          =  1  square  kilometer 


344  APPENDIX. 


TABLE  OF  VOLUMES. 

1000  cubic  millimeters  ("am)  _  i  cubic  centimeter  (ccm  or  •*) . 
1000  cubic  centimeters  =  1  cubic  decimeter  (cdm). 

1000  cubic  decimeters  =  1  cubic  meter  (cbm). 

The  volumes  of  liquids  and  gases  are  either  expressed  in  the  units 
of  the  above  table  or  in  liters.     The  liter  is  lcdm,  or 


TABLE  OF  MASSES  OR  WEIGHTS. 

10  milligrams  (m«)  =  1  centigram  (<*). 
10  centigrams  =  1  decigram  (ds). 
10  decigrams  =  1  gram  («). 

1000  grams  =  1  kilogram  or  kilo  (k). 


TABLE  OF  EQUIVALENTS. 

1  inch  =       0.0254  meter,    or  about  2|  centimeters. 
1  foot  =       0.3048  meter,    or  about  30  centimeters. 
1  yard  =       0.9144  meter,    or  about  ^  meter. 
1  mile  =  1609.0000  meters,  or  about  1T67  kilometers. 


Q"«  =  <  J.  J«  j}         a  ,itt,e  <  than  !  liter. 


1  U.S.  gallon  =  3.785  liters,  or  about  3^  liters. 

,  j  avoirdupois  i   0.02835  kilo,  n    ^i^-  J  less 

M  Troy  and  apothecaries'   c  *1   0.03110  kilo,  orratheM  more 

than  30  grams. 

1  avoirdupois  pound  =  0.45359  kilo,  or  about  T5T  kilo. 

When  great  accuracy  is  not  required,  it  will  be  found  convenient  to 
remember  that 

centimeters  X  f  =  inches  (nearly)  ; 
inches  X  f  =  centimeters  (nearly)  ; 

5  meters  =  1  rod  (nearly)  ; 

also,  kilos  X  -^  =  pounds  (nearly)  ; 

pounds         X  ^r  =  kilos  (nearly). 


APPENDIX. 


345 


SECTION    B. 


TABLES    OF    SPECIFIC    GRAVITIES    OF   BODIES. 
[The  standard  employed  in  the  tables  of  solids  and  liquids  is  distilled  water  at  4*  C.] 

I.   Solids. 


Antimony 6.712 

Bismuth 9.822 

Brass 8.380 

Copper,  cast 8.790 

Iridium 23.000 

Iron,  cast 7.210 

Iron,  bar 7.780 

Gold 19.360 

Lead,  cast 11.350 

Platinum 22.069 

Silver,  cast 10.470 

Tin,  cast 7.290 

Zinc,  cast 6.860 

Anthracite  coal 1.800 

Bituminous  coal 1.250 


Diamond 3.530 

Glass,  flint 3.400 

Human  body 0.890 

Ice 0.920 

Quartz 2.650 

Kock  salt 2.257 

Saltpetre 1.900 

Sulphur,  native 2.033 

Tallow 0.942 

Wax 0.969 

Cork 0.240 

Pine 0.650 

Oak 0.845 

Beech 0.852 

Ebony 1.187 


II.    Liquids. 


Alcohol,  absolute 0.800 

Bisulphide  of  carbon 1.293 

Ether 0.723 

Hydrochloric  acid 1.240 

Mercury 13.598 

Milk 1.032 

Naphtha 0.847 


Nitric  acid 1.420 

Oil  of  turpentine 0.870 

Olive  oil 0.915 

Sea  water 1.026 

Sulphuric  acid 1.841 

Water,  4°  C.,  distilled. . .  1.000 

Water,  0°  C. ,  distilled . . .  0.999 


III.    Gases. 

[Standard  :  air  at  0°  C. ;  barometer,  76<"°.] 


Air 1.0000 

Ammonia 0.5367 

Carbonic  acid 1.5290 

Chlorine 3.4400 

Hydrochloric  acid 1.2540 


Hydrogen 0.0693 

Nitrogen 0.9714 

Oxygen 1.1057 

Sulphuretted  hydrogen . .  1. 1912 
Sulphurous  acid 2.2474 


346 


APPENDIX. 


SECTION  C. 

TABLE  OF  NATURAL  TANGENTS. 


Deg. 

Tangent. 

Deg. 

Tangent. 

Deg. 

Tangent. 

Deg. 

Tangent. 

1 

.017 

24 

.445 

47 

1.07 

70 

2.75 

2 

.035 

25 

.466 

48 

1.11 

71 

2.90 

3 

.052 

26 

.488 

49 

1.15 

72 

3.08 

4 

.070 

27 

.510 

50 

1.19 

73 

3.27 

5 

.087 

28 

.532 

51 

1.23 

74 

3.49 

6 

.105 

29 

.554 

52 

1.28 

75 

3.73 

7 

.123 

30 

.577 

53 

1.33 

76 

4.01 

8 

.141 

31 

.601 

54 

1.38 

77 

4.33 

9 

.158 

32 

.625 

55 

1.43 

78 

4.70 

10 

.176 

33 

.649 

56 

1.48 

79 

5.14 

11 

.194 

34 

.675 

57 

1.54 

80 

5.67 

12 

.213 

35 

.700 

58 

1.60 

81 

6.31 

13 

.231 

36 

.727 

59 

1.66 

82 

7.12 

14 

.249 

37 

.754 

60 

1.73 

83 

8.14 

15 

.268 

38 

.781 

61 

1.80 

84 

9.51 

16 

.287 

39 

.810 

62 

1.88 

85 

11.43 

17 

.306 

40 

.839 

63 

1.96 

86 

14.30 

18 

.325 

41 

.869 

64 

2.05 

87 

19.08 

19 

.344 

42 

.900 

65 

2.14 

88 

28.64 

20 

.364 

43 

.933 

66 

2.25 

89 

57.29 

21 

.384 

44 

.966 

67 

2.36 

90 

Infinite. 

22 

.404 

45 

1.000 

68 

2.48 

23 

.424 

46 

1.036 

69 

2.61 

347 


SECTION   D. 

REFERENCE  TABLE  OF  RELATIVE  RESISTANCES,  ETC. 

Rel.  Resist. 

Silver @0°C 1.00  

Copper "       1.06  

Zinc "       3.74   

Platinum "       6.02   

Iron    "       6.46  

German  silver "       13.91..... 

Mercury " 63.24   


K. 

9.15 
9.72 
34.2 
55.1 
59.1 
127.3 
578.6 


Rel.  Resist. 

Nitric  Acid  —  commercial ....  @  15°  to  28°  C 1,100,000 

Sulphuric  Acid,  1  to  12  parts  water    "     2,000,000 

Common  salt  —  saturated  sol.  "     3,200,000 

Sulphate  Copper  "  "     18,000,000 

Distilled  water not  less  than  10,000,000,000 

Glass @  200°  C 15,000,000,000,000 

Gutta  percha @     0°  C. .  .5,000,000,000,000,000,000,000 


INDEX. 


[NUMBERS  REFER  TO  PAGES.] 


Aberration,  Chromatic,  323. 

Spherical,  313. 
Action  and  reaction,  14. 
Adhesion,  25. 
Air-pump,  41. 

Sprengel,  43. 

Amalgamating  battery  zincs,  162. 
Ampere,  The,  172. 
Ampere's  rule,  158. 
Ampere-volt,  The,  172. 
Atmosphere,  29. 

Atmospheric  pressure,  measurement 
of,  33. 

B. 

Barometer,  mercurial,  34. 

Aneroid,  35. 
Batteries  of  different  kinds,  164. 

of  high  resistance,  186. 

of  low  resistance,  186. 
Batteries,  Storage,  209. 
Battery,  what  constitutes  a  voltaic,  185. 
Beats  in  music,  261. 
Boyle's  or  Mariotte's  law,  40. 
Buoyant  force  of  fluids,  56. 

C. 

Calorie,  The,  141. 
Camera,  Photographer's,  335. 
Capillary  phenomena,  27. 
Celestial  chemistry  and  physics,  322. 
Center  of  gravity  defined,  82. 

of  gravity,  how  found,  83. 
Centrifugal  and  centripetal  forces,  92. 
Cohesion,  20. 

Cold,  Methods  of  producing,  artificially, 
144. 


Color,  Cause  of,  revealed  by  dispersion. 
317. 

produced  by  absorption,  324. 

produced  by  interference,  329. 
Colors,  Complementary,  329. 

Effect  of  contrast,  329. 

Effect  of  mixing,  326. 

Sky,  325. 

Component  forces,  72. 
Composition  of  parallel  forces,  75. 
Compressibility  of  gases,  38. 
Condenser,  Air,  44. 
Conduction  of  heat,  125. 
Convection  in  gases,  126. 

in  liquids,  129. 
Coulomb,  The,  171, 172. 
Couple,  Mechanical,  78. 
Critical  angle,  302. 
Crystallization,  20. 
Crystals,  21. 
Curvilinear  motion,  92. 
Currents,  Attraction  and  repulsion  be- 
tween, 192. 

Extra,  202. 

Induced,  200,  202. 

Laws  of,  193,  194. 

Laws  of  induced,  202. 

Thermo-electric,  222. 

D. 

Density,  8,  59. 

Specific,  60. 
Dew-point,  140. 

Diathermancy  and  athermancy,  330. 
Discord  in  music,  262. 
Distillation,  138. 
Divided  circuits,  184. 
Dynamo  as  an  electric  motor,  208. 

Uses  of,  208. 


350 


INDEX. 


Dynamo-electric  machine,  205. 
Dynamometers,  13. 
Dyne,  The,  106. 
Ductility,  25. 


Ear,  The,  279. 
Elasticity,  24. 

of  gases,  38. 

Electrical  measurements,  171. 
Electric  battery  defined,  157. 
Electrification,  226. 

confined  to  the  external  surface,  235. 

Two  kinds  of,  229. 
Electric  condenser,  234. 

current,  chemical  effects  of,  166. 

current,  heating  and  luminous  effects 
of,  166. 

current,  magnetic  effects  of,  170. 
*     current,  physiological  effects  of,  169. 

current,  direction  of,  157. 

discharge,  231. 

energy,  how  it  originates,  137. 

induction,  230. 

insulation,  232. 

machine,  232. 

motor,  204. 

Electricity,  Conductors  and  non-con- 
ductors of,  157. 

Static,  225. 

Two  states  of,  227. 
Electro-chemical  series,  161. 
Electrolysis,  167. 
Electro-motive  force,  159. 

force  of  different  batteries,  182. 
Electrophorus,  233. 
Electroplating     and     electrotyping, 

214,  215. 

Electroscope,  226. 
Energy,  5.  e 

Distinction  between  force  and,  102. 

Formulas  for  calculating  kinetic,  103, 
107. 

Kinetic  and  potential,  100. 

received  from  the  sun,  281. 

Transformation,  correlation,  and  con- 
servation of,  147. 

Unit  of,  101. 
Equilibrant,  77. 


Equilibrium,  13. 

of  moments,  77. 

Three  states  of,  84. 
Erg,  The,  106. 

Ether,  a  medium  of  motion,  282. 
Ether-waves,  Heating   and  chemical 

effects  of,  322. 
Evaporation,  139. 
Expansion,  Abnormal,  132. 

of  solids,  liquids,  and  gases,  130. 
Eye,  The  human,  336. 


F. 


Falling  bodies,  laws  of,  89. 

bodies,  velocity  of,  independent  of 

mass,  90. 
Flexibility,  24. 
Foot-pound,  101. 
Fluids,  9. 
Force,  11, 14. 

Centripetal  and  centrifugal,  92. 

Effect  of  a  constant,  86. 

graphically  represented,  70. 

how  measured,  12. 

Moment  of,  77. 
Forces,  Composition  of,  72. 

Equilibrant  of,  77. 

Resolution  of,  73. 

Resultant  of,  72. 

O. 


Galvanometer,  174. 

Tangent,  175. 

with  astatic  needle,  175. 
Galvanoscope,  158. 
Geissler  tube,  203. 
Gramme-dynamo,  205. 
Gravitation  and  gravity,  15 

Law  of  universal,  16. 

H. 


Hardening  and  annealing,  23. 
Hardness,  22. 

Heat,  Artificial  sources  of,  122. 

generated  by  solidification  and  lique- 
faction, 143. 
Latent,  142. 

Mechanical  equivalent  of,  148. 
Theory  of,  121. 


INDEX. 


351 


Heat,  The  sun  as  a  source  of,  123. 

unit,  141. 

Holtz  machine,  160. 
Horse-power,  105. 
Hydrometers,  62. 


Images,  286. 

formed  by  lenses,  309. 

formed  through  apertures,  286. 

Virtual,  293. 
Impenetrability,  2. 
Incandescence,  283. 
Induction  coil,  Ruhmkorff's,  202. 
Induced    currents,  characteristics   of, 

204. 
Inertia,  70. 

J. 

Joule's  equivalent,  148. 
experiment,  147. 

K. 

Kinetic  energy,  100. 


Lamp,  Brush,  212. 

Electric,  211. 

Incandescent  electric,  213. 
Latent  heat,  142. 
Lenses,  305. 

Achromatic,  323. 

Effects  of,  307. 
Leyden  jar,  234. 
Light  defined,  283. 

Electric,  210. 
Lightning,  236. 

rods,  236. 
Light-waves,  Reflection  of,  292. 

Sources  of,  283. 

Velocity  of,  292. 
Liquefaction,  136. 
Locomotive,  The,  152. 
Luminous  and  illuminated  objects,  285. 

M. 

Machines,  General  law  of,  111. 

Uses  of,  108,  110. 
Magnet,  Ampere's  theory  of,  195. 


Magnets,  Coercive  force  of,  191. 

Forms  of  artificial,  192. 

Law  of,  190. 

Polarity  of,  191. 
Magnetic  equator,  198. 

field,  196. 

force,  lines  of,  196. 

needle,  dip  of,  198. 

needle,  variation  of,  198. 

poles  of  the  earth,  197. 

transparency  and  induction,  190. 
Malleability,  25. 
Manipulation,  2. 
Manometric  flames,  268. 
Mass,  defined,  7. 
Matter,  Theory  of  its  constitution,  7. 

What  is  it,  1. 
Microphone,  The,  221. 
Microscope,  Compound,  333. 

Simple,  312. 

Minuteness  of  particles  of  matter,  6. 
Mirrors,  concave,  294. 

convex,  297. 

plane,  293. 
Mixing  colors,  effects  of,  326. 

pigments,  effects  of,  328. 
Molar  forces,  19. 
Molecular  forces,  18, 19. 
Moment  of  a  force,  77. 
Momentum,  67. 

its  relation  to  force,  67. 
Motion,  First  Law  of,  69. 

Graphical  representation  of,  70. 

Relative,  10. 

Second  Law  of,  71. 

Third  Law  of,  80. 
Musical  instruments,  270. 

scale,  259. 


Nodes,  240. 


N. 


O. 


Ohm,  174, 178. 

O^m's  law,  182. 

Overtones  and  harmonics,  262. 

P. 

Pendulum,  Laws  of,  95. 
Phonograph,  The,  277. 


352 


INDEX. 


Phosphorescence,  283. 

Photometry,  289. 

Physics  defined,  1. 

Pitch,  Musical,  259. 

Polarization  of  electric  elements,  164. 

Pores  and  porosity,  7. 

Potential,  Electric,  159. 

Press,  Hydrostatic,  60. 

Pressure,  Atmospheric,  29. 

in  fluids,  29,  51. 

transmitted  by  fluids,  47. 
Prisms,  Optical,  305. 
Pump,  Air,  41. 

Force,  46. 

Lifting  or  suction,  44. 

Pump,  Sprengel,  43. 

Q. 

Quality  of  sound,  265. 


Radiant  energy,  281. 
Radiation,  129. 

Only  one  kind  of,  322. 

Thermal  effects  of,  330. 
Radiometer,  281. 
Rainbow,  The,  315. 
Ray,  beam,  and  pencil  defined,  284. 
Reflection,  Total,  302. 
Refraction,  298. 

Cause  of,  300. 

Double,  304. 

Index  of,  300,  301. 
Relay  and  repeater,  217. 
Resistance  measured  by  substitution, 
179. 

of  battery,  178. 

of  electric  conductors,  176. 
Resonators,  253. 
Rheostat,  Description  of,  178. 


S. 

Shadows,  287. 
Shunts,  184. 
Siphon,  54. 
Sonometer,  260. 
Sound,  Analysis  of,  265. 
defined,  247. 


Sound,  Intensity  of,  251. 

Quality  of,  265. 

Synthesis  of,  266. 

Sounding-plates  and  bells,  273-275. 
Sound-vibrations,  Method  of  repre- 
senting graphically,  267. 
Sound- waves,  How  they  originate,  244. 

How  they  travel,  245. 

Measuring  length  and  velocity  of,  255 

Media  for  transmitting,  247. 

Reinforcement  and  interference  of, 
253,  256. 

Reflection  of,  249. 

Velocity  of,  248. 
Speaking-tubes,  252. 
Specific  gravity  and  specific  density,  69. 

Formulas  for,  60. 
Spectra,  314. 

Bright-line,  318. 

Dark-line,  320. 

Continuous,  318. 
Spectrum  analysis,  321. 
Stability  of  a  body,  on  what  it  depends, 

85. 
Steam-engine,  Compound,  152. 

Condensing  and  non-condensing,  151. 

Description  of  simple,  149. 
Stereopticon,  338. 
Storage  batteries,  209. 
Surface  of  a  liquid  at  rest  is  level,  53. 
Synthesis  of  white  waves,  316. 


T. 


Telescope,  Astronomical,  335. 
Telegraph,  The,  216. 
Telephone,  The  Bell,  218. 
Temperature,  defined,  124. 

distinguished  from  quantity  of  heat, 

124. 

Temperatures,  Standard,  133. 
Tenacity,  20. 
Tension,  26. 

Theory  of  exchanges,  332. 
Thermo-dynamics  defined,  147. 
Thermo-electric  batteries  and  ther. 
mopiles,  224. 

currents,  222. 

series,  224. 
Thermometer,  Construction  of,  133= 

Graduation  of,  133. 


INDEX. 


353 


Thermometry,  133. 
Three  states  of  matter,  9. 
Transformation  of    electric  energy, 

208. 

of  electric  energy  into  heat,  189. 
of  heat  energy  into  electric  energy, 

222. 

of  mechanical  energy  into  electric  po- 
tential energy,  225. 

Transparency,      translucency,      and 
opacity,  285. 

U. 

Undulatory  theory  of  radiation,  283. 
Unit  of  heat,  141. 

of  intensity  of  a  magnetic  field,  173. 

of  magnetic  pole,  173. 
Units,  Absolute,  106. 

C.G.8.  magnetic  and  electro-magnetic, 
173. 

Fundamental  and  derived,  106. 


V. 

Vaporization,  136. 
Ventilation,  128. 
Vibration  of  strings,  260. 

Period  of,  238. 

Vibrations    forced    and    sympathetic, 
257. 

Graphical  method  of  studying,  243. 

Propagation  of,  239. 

Stationary,  240. 


Viscosity,  24. 
Visual  angle,  291. 
Vocal  organs,  276. 
Volt,  The,  172. 
Voltaic  arc,  210. 

cells,  best  arrangement  of,  187. 

cells  connected  in  opposition,  185. 

cells,  methods  of  combining,  185. 
Volume,  7. 


W. 

Watt,  172. 
Waves,  239. 

Amplitude  of,  239. 

how  propagated,  243 

Interference  of,  239. 

Length  of,  239. 

Longitudinal  and  transverse.  241,  242. 

Reflection  of,  239. 
Wave-motion,  Air  as  a  medium  of, 

242. 
Weight,  16. 

Point  of  maximum,  17. 
Welding,  20. 
Wheatstone  bridge,  180. 
Work,  98. 

Formula  for  estimating,  99. 

Rate  of  doing,  104. 

Unit  of,  101. 

wasted,  103. 


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Taylor   Elements  of  the  Calculus 1.80 

Wentworth      Grammar  School  Arithmetic    75 

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jVentworth  &  Hill :  Practical  Arithmetic 1.00 

Abridged  Practical  Arithmetic 75 

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Part  II.  Examination  Manual 35 

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Exercises  in  Geometry 70 

Five-place  L*g.  and  Trig.  Tables  (i  Tables)      .50 

Five-place  Log.  and  Trig.  Tables  (  d)mp.  Ed. )  1.00 

Wentworth  &  Reed :  First  Steps  in  Number,  Pupils'1  Edition       .30 

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